Systems and methods for tuning a mhz rf generator within a cycle of operation of a khz rf generator

ABSTRACT

Systems and methods for tuning a megahertz radio frequency (RF) generator within a cycle of operation of a kilohertz (kHz) RF generator are described. In one of the methods, a predetermined periodic waveform is provided to a processor. The processor uses a computer-based model to determine plurality of frequency parameters for the predetermined periodic waveform. The frequency parameters are applied to the megahertz RF generator to generate an RF signal having the frequency parameters during one or more cycles of operation of the kilohertz RF generator.

FIELD

The present embodiments relate to systems and methods for tuning amegahertz (MHz) radio frequency (RF) generator during a cycle ofoperation of a kilohertz (kHz) RF generator.

BACKGROUND

The background description provided herein is for the purposes ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

In a plasma tool, one or more radio frequency (RF) generators arecoupled to an impedance matching circuit. The impedance matching circuitis coupled to a plasma chamber. RF signals are supplied from the RFgenerators to the impedance matching circuit. The impedance matchingcircuit outputs an RF signal upon receiving the RF signals. The RFsignal is supplied from the impedance matching circuit to the plasmachamber for processing a wafer in the plasma chamber. During processingof the wafer, an amount of power is reflected from plasma of the plasmachamber via the impedance matching circuit towards the one or more RFgenerators. The reflected power reduces efficiency in processing thewafer and also causes damage to the one or more RF generators.

It is in this context that embodiments described in the presentdisclosure arise.

SUMMARY

Embodiments of the disclosure provide apparatus, methods and computerprograms for tuning a megahertz (MHz) radio frequency (RF) generatorduring a cycle of operation of a kilohertz (kHz) RF generator. It shouldbe appreciated that the present embodiments can be implemented innumerous ways, e.g., a process, an apparatus, a system, a piece ofhardware, or a method on a computer-readable medium. Several embodimentsare described below.

Several plasma etch systems operate with two different RF frequencies,one lower, such as 400 kilohertz (kHz), and one more than 100 timeshigher, e.g., 60 megahertz (MHz). A load impedance for the higher RFfrequency may be strongly modulated by the lower RF frequency. Amatching network for each RF frequency is tuned using one variablecapacitor plus a variable RF frequency. For example, the higher RFfrequency is tuned to a value in a range between 57 MHz and 63 MHz. Asingle value of the load impedance can be tuned to have a voltagereflection coefficient Γ near zero, but because an impedance of thehigher RF frequency varies with a phase of the low frequency RF, it isdifficult to determine a single combination of the variable capacitorand the higher RF frequency that works for all portions of a cycle ofthe lower RF frequency. Without the single combination, a time-averagedpower reflection coefficient Γ² can be as high as 50%.

In one embodiment, a method is provided in which the higher RF frequencyhas an average value plus a variation around the average value. Thevariation is periodic with the lower RF frequency and has apredetermined functional form. For example, the variation is a squarewave with an amplitude and a phase relative to the lower RF frequency.As another example, the variation is a sinusoidal function or arectangular function. As yet another example, the variation is atrapezoidal function with high and low frequency segments connected byfrequency ramps.

In a first embodiment, a method for determining frequency parameters andmatch network parameters is provided for controlling an RF generator ofthe higher frequency. In the first embodiment, the following operationsare performed:

-   -   1. A plasma tool detects a frequency and phase of a waveform of        the lower frequency. As an example, the lower frequency is        detected by querying an RF generator of the lower frequency and        a phase of the lower frequency is deduced from detecting voltage        zero crossings of the lower frequency.    -   2. The plasma tool uses a sensor and fast data acquisition to        save waveforms of the higher frequency measured between the RF        generator of the higher frequency and the matching network over        a time period of one or a few cycles of the lower frequency. As        an example, the sensor measures complex voltage and current.    -   3. A computer calculates an instantaneous complex voltage        reflection coefficient Γ for a number of short, e.g., about 0.1        microsecond, time intervals. The computer also calculates an        average power reflection coefficient Γ² associated with the RF        generator of the higher frequency over a period of the lower        frequency.    -   4. The computer calculates a set of optimum parameters to        minimize a predicted value of the average power reflection        coefficient. For example, the computer:        -   a. Divides a measured voltage waveform of the lower            frequency into short segments of about 0.1 microseconds each            to generate approximately 25 short segments per period of            the lower frequency.        -   b. Calculates the complex voltage reflection coefficient Γ            of the higher frequency for each segment.        -   c. Applies a computer-based model of an RF path of the            plasma tool to calculate a load impedance for each segment            from the complex voltage reflection coefficient Γ. Inputs to            the calculation include a known RF frequency and variable            capacitor values.        -   d. For a predetermined functional form of the higher            frequency, calculates a set of frequency parameters, which            minimize a period-averaged reflection coefficient associated            with the RF generator of the higher frequency. As an            example, the frequency parameters include:            -   i. A constant average frequency of the RF generator of                the higher frequency.            -   ii. An amplitude of a trapezoidal frequency variation.            -   iii. Durations of high and low sections of the                trapezoidal frequency variation, and            -   iv. A phase of the trapezoidal frequency variation                relative to the phase of the lower frequency,    -   5. The optimization to minimize an average power reflection        coefficient includes a value of the variable capacitor as well        as the higher frequency.    -   6. The computer applies the frequency variation.    -   7. The computer iterates the operations 2 through 5. After        applying the method, a power reflection coefficient at the RF        generator of the higher frequency decreases to about 3% from        about 35%.

In a second embodiment, a method is provided to reduce a voltagereflection coefficient and power reflection coefficient at an input ofthe computer-based model. The method is executed during recipedevelopment to determine operation parameters, and the operationparameters are applied during processing of a substrate. In the method,the following operations are performed:

-   -   1. A fast data acquisition device and the sensor are installed        during recipe development and are not used on production tools        during the processing to reduce difficulties and time associated        with using the fast data acquisition device and the sensor. An        example of a fast data acquisition device includes an        oscilloscope.    -   2. During the recipe development, two operations are performed:        -   a. A tuning operation, which determines a value of an            average frequency to be applied to an RF generator of the            higher frequency.        -   b. A fast data sensing, acquisition, and computer analysis            operation, which determines a frequency variation in the            average frequency. As an example, the two operations are            executed to minimize an average voltage reflection            coefficient, for which positive and negative values can            average to zero. This means the average voltage reflection            coefficient can be zero even though an average power            reflection coefficient may be large. To further illustrate,            an operation of choosing the frequency variation coincides            with an operation for determining the average frequency. The            frequency variation around the average frequency is            determined simultaneously with the operation for determining            the average frequency. For multiple RF generators, the            average frequency is determined by minimizing a portion of            reflected power at the fundamental frequency while ignoring            the remaining portion of the reflected power at one or more            modulated sideband frequencies of the reflected power. This            is equivalent to minimizing a Fourier peak of the reflected            power at the fundamental frequency, or to minimizing the            average voltage reflection coefficient, which is a complex            number, for which positive and negative parts cancel each            other.    -   3. During the recipe development, the average frequency and        frequency variation are determined in a manner that is the same        as that described above in the first embodiment, with an        additional constraint that the average voltage reflection        coefficient be simultaneously minimized    -   4. The computer stores the frequency parameters.    -   5. During the processing, for a given recipe, a tool-to-tool        variation or wafer-to-wafer variation is in an average value of        the higher frequency. The average frequency determined during        the recipe development is applied during the processing to        minimize an average voltage reflection coefficient. Then, on top        of the average frequency, a frequency variation previously        determined for that recipe, is applied from tool-to-tool or        wafer-to-wafer. A timing and duration of the frequency variation        is synchronized with a zero-crossing and period of the RF        generator of the lower frequency. In the second embodiment,        there is no use of the fast data acquisition device and/or the        sensor during processing.

In an embodiment, a method is provided in which the higher RF frequencyis tuned in two parts. The first part determines an average value of thehigher RF frequency, which will remain constant for many cycles of thelower RF frequency. The second part determines fast variations aroundthe average value to be applied within a cycle of the lower RFfrequency.

In a third embodiment, a method is described to reduce power reflectioncoefficient for each bin within a cycle of the lower RF frequency. Thelower RF frequency is divided into multiple bins. There is nopredetermined functional form used in the third embodiment. Thefollowing operations are performed in the third embodiment:

-   -   1. During recipe development, the computer executes a fast        frequency variation operation by sub-dividing a period or cycle        of the lower RF frequency into a number of shorter time bins.        For example, the period of the lower RF frequency is divided        into 16 bins. A length or a time period of each bin depends on a        value of the lower RF frequency. An example of the lower RF        frequency is a frequency ranging from 340 kHz to 440 kHz.    -   2. During recipe development, the computer applies the        computer-based model to minimize an average power reflection        coefficient for the bins by varying:        -   a. the variable capacitor to determine a capacitance,        -   b. an average frequency of the higher RF frequency,        -   c. a frequency variation from the average frequency, and        -   d. subject to a constraint that an average voltage            reflection coefficient is also minimized    -   3. During tool operation in which a substrate is processed, an        assumption is made that for a given recipe, the tool-to-tool or        wafer-to-wafer variations are in an average value of the higher        RF frequency.    -   4. Also, during the tool operation, on top of the average        frequency of the higher RF frequency, the frequency variation        previously determined for that recipe is applied by the computer        from bin to bin. A timing and duration of the frequency        variation is synchronized by the computer with a zero-crossing        and period of the lower RF frequency. Also, during the tool        operation, the capacitance determined during the recipe        development is applied for all bins of the lower RF frequency.

In one embodiment, a tuning method is described. The tuning methodincludes accessing, for a first set of one or more cycles of operationof a first radio frequency generator, a plurality of reflectionparameter values associated with a second radio frequency generator. Thetuning method further includes calculating a plurality of load impedanceparameter values from the plurality of reflection parameter values byapplying the plurality of reflection parameter values to acomputer-based model of at least a portion of a radio frequency path.The radio frequency path is between the second radio frequency generatorand an electrode of a plasma chamber. The tuning method also includesreceiving a plurality of frequency modulation parameters of a radiofrequency signal to be generated by the second radio frequencygenerator. The tuning method further includes determining values of theplurality of frequency modulation parameters by applying the pluralityof load impedance parameter values to the computer-based model. Thevalues of the plurality of frequency modulation parameters aredetermined to minimize a reflection coefficient parameter at an input ofthe computer-based model. The tuning method includes controlling thesecond radio frequency generator according to the values of theplurality of frequency modulation parameters during a second set of oneor more cycles of operation of the first radio frequency generator.

In an embodiment, a tuning method is described. A portion of the tuningmethod is executed during recipe development and another portion of thetuning method is executed during processing. The portion executed duringthe recipe development includes accessing, for a set of one or morecycles of operation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator. Moreover, the portion executed during the recipe developmentfurther includes calculating a plurality of load impedance parametervalues from the plurality of reflection parameter values by applying theplurality of reflection parameter values to a computer-based model of atleast a portion of a radio frequency path. The radio frequency path isbetween the second radio frequency generator and an electrode of aplasma chamber. The portion executed during the recipe development alsoincludes receiving a plurality of frequency modulation parameters of aradio frequency signal to be generated by the second radio frequencygenerator. The portion executed during the recipe development furtherincludes determining values of the plurality of frequency modulationparameters by applying the plurality of load impedance parameter valuesto the computer-based model. The values of the plurality of frequencymodulation parameters are determined to minimize one or more reflectioncoefficient parameters at an input of the computer-based model. Theother portion of the method is executed during processing of a substratewithin another plasma chamber. The other portion of the method includescontrolling a third radio frequency generator according to the values ofthe plurality of frequency modulation parameters determined during therecipe development. The operation of controlling the third radiofrequency generator is performed during a set of one or more cycles ofoperation of a fourth radio frequency generator.

In an embodiment, a tuning method is described. A portion of the tuningmethod is executed during recipe development and another portion of thetuning method is executed during processing. The portion executed duringthe recipe development includes accessing, for a set of one or morecycles of operation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator. The portion executed during the recipe development furtherincludes calculating a plurality of load impedance parameter values fromthe plurality of reflection parameter values by applying the pluralityof reflection parameter values to a computer-based model of at least aportion of a radio frequency path between the second radio frequencygenerator and an electrode of a plasma chamber. The portion executedduring the recipe development also includes receiving a plurality offrequency modulation parameters of a radio frequency signal to begenerated by the second radio frequency generator, wherein the pluralityof frequency modulation parameters include a frequency variation of theradio frequency signal. The portion executed during the recipedevelopment further includes determining values of the plurality offrequency modulation parameters by applying the plurality of loadimpedance parameter values to the computer-based model. The values ofthe plurality of frequency modulation parameters are determined tominimize one or more reflection coefficient parameters at an input ofthe computer-based model. The other portion of the method is executedduring processing of a substrate within another plasma chamber. Theother portion of the method includes controlling a third radio frequencygenerator according to the values of the plurality of frequencymodulation parameters determined during the recipe development. Theoperation of controlling the third radio frequency generator includesapplying the values of the plurality of frequency modulation parametersto a baseline frequency of operation of the third radio frequencygenerator.

In an embodiment, a tuning method is described. A portion of the tuningmethod is executed during recipe development and another portion of thetuning method is executed during processing. The portion executed duringthe recipe development includes accessing, for a set of one or morecycles of operation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator. Each of the plurality of reflection parameter valuescorresponds to a bin of each of the one or more cycles of operation ofthe first radio frequency generator. The portion executed during therecipe development further includes calculating a plurality of loadimpedance parameter values from the plurality of reflection parametervalues by applying the plurality of reflection parameter values to acomputer-based model of at least a portion of a radio frequency path.The radio frequency path is between the second radio frequency generatorand an electrode of a plasma chamber. The portion executed during therecipe development also includes determining values of a plurality offrequency modulation parameters by applying the plurality of loadimpedance parameter values to the computer-based model. The values ofthe plurality of frequency modulation parameters are determined tominimize a plurality of values of a reflection coefficient parameter atan input of the computer-based model for each of the bins. The otherportion of the method is executed during processing of a substratewithin another plasma chamber. The other portion of the method includescontrolling a third radio frequency generator according to the values ofthe plurality of frequency modulation parameters determined during therecipe development. The operation of controlling the third frequencygenerator is performed during a set of one or more cycles of operationof a fourth radio frequency generator.

Some advantages of the herein described systems and methods includefinding values of the higher RF frequency and of the variable capacitorthat reduces power and/or voltage that is reflected towards themegahertz RF generator during each cycle of operation of the kilohertzRF generator. Additional advantages include reducing a number of sensorsand fast data acquisition devices during processing of a substrate. Forexample, in the second and third embodiments, there is no need to usethe fast data acquisition devices and sensors after recipe development.Once a recipe having the values of the higher RF frequency and of thevariable capacitor is determined, the recipe is applied duringprocessing of the substrate. There is no need to again measure a complexvoltage and current during the processing of the substrate.

Further advantages include applying the predetermined functional form.The application of the predetermined functional form simplifies adetermination of the frequency parameters and an application of theoperation parameters. It is easy to control the RF generator of thehigher frequency to follow the predetermined functional form.

Moreover, when the computer-based model is used, there is no need to usea sensor on the RF path. For example, the sensor is not coupled to an RFtransmission line or an output of the impedance matching network.Rather, a complex voltage and current is measured by a sensor coupled toan output of the megahertz RF generator and is propagated via thecomputer-based model to facilitate a determination of the values of thehigher frequency and the variable capacitor. It is more difficult andtime-consuming to use the sensor on the RF path than to use thecomputer-based model.

Other aspects will become apparent from the following detaileddescription, taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments are understood by reference to the following descriptiontaken in conjunction with the accompanying drawings.

FIG. 1A is a diagram of an embodiment of a system to illustrate adetermination of values of a voltage reflection coefficient over one ormore cycles of operation of an X kilohertz radio frequency (RF)generator.

FIG. 1B-1 is an embodiment of a table to illustrate that values of thevoltage reflection coefficient are determined based on a complex voltageand current that is obtained at periodic time intervals over a cycle ofoperation of the X kilohertz RF generator.

FIG. 1B-2 is an embodiment of a graph to illustrate a correspondencebetween the values of the voltage reflection coefficient and timeintervals during a cycle of an RF signal generated by the X kilohertz RFgenerator.

FIG. 1C is a diagram of an embodiment of an RF path model to illustratecalculation of load impedance values from the values of the voltagereflection coefficient.

FIG. 1D-1 is a diagram of an embodiment of the RF path model toillustrate a determination of operation parameters, which includefrequency parameters and match network parameters, based on applicationof the load impedance values at an output of the RF path model tominimize an average power reflection coefficient at an input of the RFpath model.

FIG. 1D-2 is an embodiment of a graph to illustrate multiple cycles ofan RF signal that is generated by an X kilohertz RF generator.

FIG. 1D-3 is a diagram of an embodiment of a system to apply values ofthe operation parameters during a set of cycles of operation of the Xkilohertz RF generator of FIG. 1 during processing of a substrate.

FIG. 2A is an embodiment of a graph to illustrate a cycle of an RFsignal.

FIG. 2B is an embodiment of a graph to illustrate a forward voltagewaveform of an RF signal that is supplied by a Y megahertz (MHz) RFgenerator.

FIG. 2C is an embodiment of a graph to illustrate a reverse voltagewaveform of the RF signal that is supplied by the Y MHz RF generator.

FIG. 2D is a diagram of an embodiment of a graph to illustrate theforward voltage waveform and the reverse voltage waveform in one graph.

FIG. 2E is an embodiment of a Smith chart to illustrate values of avoltage reflection coefficient at an output of a Y MHz RF generatorbefore applying the methods described herein.

FIG. 3A is a diagram of an embodiment of a graph to illustrate acomparison between a frequency of an RF signal that is output from a Ymegahertz RF generator after applying the methods described herein andan RF signal that is output from the Y megahertz RF generator beforeapplying the methods.

FIG. 3B is an embodiment of a Smith chart to illustrate values of avoltage reflection coefficient at an output of a Y MHz RF generatorafter applying the methods described herein.

FIG. 4A is a diagram of an embodiment of a system to illustrate that themethods described above with respect to FIG. 1A are applicable to thesystem of FIG. 4A during recipe development instead of during processingof a substrate.

FIG. 4B is a diagram of an embodiment of the table, which is generatedby a processor during recipe development in the same manner in which thetable of FIG. 1B-1 is generated by the processor during processing ofthe substrate.

FIG. 4C is a diagram of an embodiment of the RF path model to illustrategeneration of the load impedance values from the values of the voltagereflection coefficient for or during recipe development.

FIG. 4D is a diagram of an embodiment to illustrate a determination ofthe values of the operation parameters for or during recipe development.

FIG. 4E is a diagram of an embodiment of a system to illustrate anapplication, during processing, of the values of the operationparameters that are determined during recipe development.

FIG. 5A is a diagram of an embodiment of a system to illustrategeneration of the values of the voltage reflection coefficient by theprocessor during recipe development for each bin of a cycle of operationof the X kilohertz RF generator.

FIG. 5B is a diagram of an embodiment of a table that is generated bythe processor for recipe development for each bin of one or more cyclesof operation of the X kilohertz RF generator.

FIG. 5C is a diagram of an embodiment of the RF path model to illustrategeneration of the load impedance values for each bin of the cycle ofoperation of the X kilohertz RF generator from the values of the voltagereflection coefficient during recipe development.

FIG. 5D is a diagram of an embodiment of the RF path model to illustratea determination of values of the operation parameters for which valuesof the power reflection coefficient for the bins of the cycle ofoperation of the X kilohertz RF generator are minimized during recipedevelopment.

FIG. 5E is a diagram of an embodiment of a system to illustrate use ofthe operation parameters for each bin during processing of a substrate.

DETAILED DESCRIPTION

The following embodiments describe systems and methods for tuning amegahertz (MHz) radio frequency (RF) generator during a cycle ofoperation of a kilohertz (kHz) RF generator. It will be apparent thatthe present embodiments may be practiced without some or all of thesespecific details. In other instances, well known process operations havenot been described in detail in order not to unnecessarily obscure thepresent embodiments.

FIG. 1A is a diagram of an embodiment of a system 100, such as a plasmatool, to illustrate a determination of values of a voltage reflectioncoefficient over one or more cycles of operation of an X kilohertz RFgenerator 112. The system 100 includes the X kilohertz RF generator 112,a Y megahertz RF generator 114, a computer 118, and a plasma chamber108. The system 100 also includes an impedance matching network 110, asensor 120, and a fast data acquisition device 121. An example of thesensor 120 is a voltage sensor and an example of a fast data acquisitiondevice is a digital storage oscilloscope. Another example of a fast dataacquisition device is a fast data acquisition circuit board. The sensor120 and the fast data acquisition device 121 together measure forwardvoltage and reverse voltage. To illustrate, the sensor 120 and the fastdata acquisition device 121 measure a forward voltage amplitude, areverse voltage amplitude, and a phase between the forward voltageamplitude and the reverse voltage amplitude. It should be noted that theterms reverse voltage and reflected voltage are used hereininterchangeably.

An example of an X kilohertz RF generator, as described herein, includesa 400 kHz RF generator or another RF generator that operates inkilohertz frequencies. An example of a Y megahertz RF generator, asdescribed herein, include a 2 MHz RF generator or a 13.56 MHz RFgenerator or a 27 MHz RF generator or a 60 MHz RF generator. Examples ofa computer, described herein, include a desktop computer, a laptopcomputer, a smart phone, and a tablet.

The computer 118 includes a processor 126 and a memory device 128. Theprocessor 126 is coupled to the memory device 128 and is also coupled tothe RF power supplies 122 and 124. As used herein, instead of aprocessor, a central processing unit (CPU), a controller, an applicationspecific integrated circuit (ASIC), or a programmable logic device (PLD)is used, and these terms are used interchangeably herein. Examples of amemory device include a read-on1y memory (ROM), a random access memory(RAM), a hard disk, a volatile memory, a non-volatile memory, aredundant array of storage disks, a Flash memory, etc. The processor 126is coupled via a cable, such as a serial transfer cable, a paralleltransfer cable, or a universal serial bus (USB) cable, to the fast dataacquisition device 121, which is coupled to the sensor 120.

An example of a fast data acquisition device, described herein, is adevice for acquiring data regarding oscillations or frequencies ofoscillations of a voltage or power of an RF signal that is output at anoutput terminal of an RF generator. The sensor 120 is coupled to anoutput O1 of the X megahertz RF generator 112 via a directional coupler.The Y megahertz RF generator 114 includes a sensor 131, such as acomplex voltage and current probe or a complex voltage sensor. Thesensor 131 is coupled to an output terminal O2 of the Y megahertz RFgenerator 114. The sensor 131 is also coupled to a fast data acquisitiondevice 123, which is coupled via a cable to the processor 126. Examplesof the cable are provided above.

The impedance matching network 106 includes one or more circuitcomponents, e.g., one or more inductors, or one or more capacitors, orone or more resistors, or a combination or two or more thereof, etc.,which are coupled with each other. For example, the impedance matchingnetwork 106 includes two branches. Each of the two branches includesmultiple circuit components that are coupled to each other in a serialor parallel manner One of the two branches is coupled to the X kilohertzRF generator 112 and another one of the two branches coupled to the Ymegahertz RF generator 114 and the branches are coupled to an output ofthe impedance matching network 106. It should be noted that the termsimpedance matching network, a match, impedance matching circuit, a matchcircuit, and match network are used herein interchangeably.

An example of the plasma chamber 108 is a capacitive1y coupled (CCP)plasma chamber in which an upper electrode 106 and a bottom electrode ofa plasma excitation electrode 104 are placed in a manner to becapacitive1y coupled with each other. For example, the upper electrode106 is placed above the plasma excitation electrode 104 to form a gapbetween the upper electrode 106 and the plasma excitation electrode 104.The upper electrode 106 is coupled to a ground potential. Radiofrequency power is capacitive1y coupled between the upper electrode 106and the plasma excitation electrode 104 via the gap. Each of the lowerelectrode and the upper electrode 106 is made of a metal, e.g., anodizedaluminum, alloy of aluminum, etc.

The output terminal O1 of the X kilohertz RF generator 112 is coupled toan input terminal I1 of the impedance matching network 110 via an RFcable RFC1 and the output terminal O2 of the Y megahertz RF generator114 is coupled to another input terminal I2 of the impedance matchingnetwork 110 via another RF cable RFC2. Also, the output of the impedancematching network 110 is coupled to the bottom electrode of the plasmaexcitation electrode 104 via an RF transmission line RFT1.

The X kilohertz RF generator 112 includes the RF power supply 122, whichis an RF oscillator. Similarly the Y kilohertz RF generator 114 includesthe RF power supply 124, which is also an RF oscillator. The RFoscillator 122 is coupled to the output terminal O1 and the RFoscillator 124 is coupled to the output terminal O2. A combination ofthe RF cable RFC2, the branch of the impedance matching network 110 thatis coupled between the input I2 and the output of impedance matchingnetwork 110, the RF transmission line RFT1, and the plasma excitationelectrode 104 is referred to herein as an RF path 102. Another branch ofthe impedance matching network 110 is coupled between the input I1 andthe output of the impedance matching network 110.

A substrate S, such as a semiconductor wafer, is placed on a top surfaceof the plasma excitation electrode 104 for being processed, which mayinclude etching a layer of the substrate S, or deposition of a materialon the substrate S, or sputtering the substrate S, or cleaning thesubstrate S, or a combination thereof. During the processing of thesubstrate S, the processor 126 provides one or more power values and oneor more frequency values to the RF power supply 122 of the X kilohertzRF generator 112 and provides one or more power values and one or morefrequency values to the RF power supply 124 of the Y megahertz RFgenerator 114.

Upon receiving the power values and the frequency values, the RF powersupply 122 generates an RF signal 130 having the power values and thefrequency values, and supplies the RF signal 130 via the output O1 andthe RF cable RFC1 to the input I1 of the impedance matching network 110.Similarly, upon receiving the power values and the frequency values, theRF power supply 124 generates an RF signal 132 having the power valuesand the frequency values, and supplies the RF signal 132 via the outputO2 and the RF cable RFC2 to the input I2 of the impedance matchingnetwork 110.

The impedance matching network 110 receives the RF signals 130 and 132and matches an impedance of a load that is coupled to the output ofimpedance matching network 110 with that of a source that is coupled tothe inputs I1 and I2 of the impedance matching network 110, and combinesthe RF signals 130 and 132 to output a modified RF signal 134 at theoutput of impedance matching network 110. An example of the load coupledto the output of the impedance matching network 110 includes the plasmachamber 108 and the RF transmission line RFT1. An example of the sourcecoupled to the inputs I11 and I21 include the X kilohertz RF generator112, the Y megahertz RF generator 114, and the RF cables RFC1 and RFC2.The modified RF signal 134 is supplied via the RF transmission line RFT1and to the lower electrode of the plasma excitation electrode 104 tostrike or maintain plasma in the gap formed between the plasmaexcitation electrode 104 and the upper electrode 106 of the plasmachamber 108. The plasma of the plasma chamber 108 has RF power thatprocesses the substrate S.

During processing of the substrate S, the sensor 120 and the fast dataacquisition device 121 measure a voltage or power of the RF signal 130that is output from the X kilohertz RF generator 112 to output awaveform, such as a voltage waveform or a power waveform. The waveformthat is measured by the sensor 120 and the fast data acquisition device121 has a phase ϕ of the RF signal 130. The phase ϕ of the RF signal 130provides crossings or times at which the waveform of the RF signal 130crosses a zero value of voltage or power. The waveform of the RF signal130 is sinusoidal or substantially sinusoidal and crosses the zero valueof voltage or power at periodic time intervals.

The processor 126 receives values of the waveform that is measured bythe sensor 120 and the fast data acquisition device 121 via the cable todetermine the phase ϕ of the waveform of the RF signal 130. For example,the processor 126 determines times at which the waveform of the RFsignal 130 become zero at positive crossings and the times define thephase ϕ. At the positive crossings, the waveform of the RF signal 130transitions from a negative value to a positive value.

Also, during processing of the substrate S, the sensor 131 and the fastdata acquisition device measure a forward voltage amplitude, a reversevoltage amplitude, and a phase between the forward and reverse voltageamplitudes at the output O2 of the Y megahertz RF generator 114 andprovides the amplitudes and the phase via the cable to the processor126. The processor 126 determines based on the forward voltageamplitude, the reverse voltage amplitude, and the phase, multiple valuesΓ11, Γ21 through Γn1 of a voltage reflection coefficient over one cycle,such as one time period, of the RF signal 130, where n is an integergreater than two. For example, the processor 126 determines the valuesof the voltage reflection coefficient as a ratio of a voltage that isreflected at the output O2 towards the Y megahertz RF generator 114 to avoltage that is supplied at the output O2 from the Y megahertz RFgenerator 114. The reflected voltage is a complex number having anamplitude and a phase and the supplied voltage is also a complex numberhaving an amplitude and a phase. The terms supplied voltage and forwardvoltage are used herein interchangeably. The voltage that is reflectedtowards the Y megahertz RF generator 114 is reflected from the plasmachamber 108 via the RF path 102. The voltage that is reflected and thevoltage that is supplied at the output O2 are identified by theprocessor 126 from the forward voltage amplitude, the reverse voltageamplitude, and the phase between the amplitudes measured by the sensor131 and the fast data acquisition device 123. The processor 126 storesthe values Γ11, Γ21 through Γn1 of the voltage reflection coefficient inthe memory device 128 and accesses, such as obtains or reads, the valuesΓ11, Γ21 through Γn1 from the memory device 128. A voltage reflectioncoefficient is an example of a reflection parameter or a reflectioncoefficient parameter. Another example of the reflection parameter is acomplex voltage and current or another parameter that has a complexvalue.

In an embodiment, the processor 126 is coupled to an RF power supply ofan RF generator via a digital signal processor of the RF generator andone or more power controllers of the RF generator and one or morefrequency tuners of the RF generator. The digital signal processor iscoupled to the processor 126 and to the one or more power controllersand to the one or more frequency tuners. The power controllers controlpower values that are output from the RF power supply of the RFgenerator during different states, such as a high logic state and a lowlogic state, and the frequency tuners are controllers that controlfrequency values that are output from the RF power supply of the RFgenerator during the different states.

In one embodiment, the sensor 120 and the fast data acquisition device121 measure voltage of the RF signal 130 at the output O1. The measuredvoltage is provided to the processor 126 from the voltage sensor via acable that couples the voltage sensor to the processor 126. Theprocessor 126 determines times at which the measured voltage is zerowhile crossing a positive crossing to determine the phase ϕ of thevoltage of the RF signal 130.

In an embodiment, the sensor 120 is coupled to the output O1 of the Xkilohertz RF generator 112 for a predetermined number of initial cyclesof operation of the X kilohertz RF generator 112 or of the RF signal130. After the predetermined number of initial cycles, the sensor 120 isdisconnected from the output O1. The processor 126 determines that thephase of the RF signal 130 will continue to be the same as thatdetermined with the measured values of voltage of the RF signal 130received from the sensor 120.

In one embodiment, the sensor 131 is located outside the Y megahertz RFgenerator 114 and is coupled to the output O2 of the Y megahertz RFgenerator 114. In an embodiment, the sensor 120 is located within the Xkilohertz RF generator 112.

It should be noted that in an embodiment, instead of applying themodified RF signal 134 to the lower electrode of the plasma excitationelectrode 104 and coupling the upper electrode 106 to the groundpotential, the modified RF signal 134 is applied to the upper electrode106 and the lower electrode of the plasma excitation electrode 104 iscoupled to the ground potential.

In one embodiment, instead of coupling the upper electrode 106 to theground potential, the upper electrode is coupled to one or more RFgenerators via an impedance matching network.

In an embodiment, instead of the sensor 120, a voltage and current probe(VI probe) that measures a complex voltage and current is used. Thecomplex voltage and current includes a current amplitude, a voltageamplitude, and a phase between the current amplitude and the voltageamplitude.

In one embodiment, a cycle of operation of an RF generator occurs togenerate a cycle of an RF signal. For example, during one cycle ofoperation of an RF generator, described herein, one period of an RFsignal is generated by the RF generator.

In an embodiment, the sensor 131 and the fast data acquisition device123 measure the complex voltage and current, which includes a voltageamplitude, a current amplitude, and a phase between the voltageamplitude and the current amplitude. The sensor 131 and the fast dataacquisition device 123 provide the amplitudes and the phase via thecable to the processor 126. The processor 126 determines based on thevoltage amplitude, the current amplitude, and the phase, multiple valuesΓ11, Γ21 through Γn1 of a voltage reflection coefficient over one cycleof the RF signal 130.

In one embodiment, both the sensors 120 and 131 are coupled to the samefast data acquisition device 121 or 123.

In an embodiment, the terms values and amounts are used hereininterchangeably. For example, the terms values of frequency modulationparameters and amounts of frequency modulation parameters are usedherein interchangeably. To illustrate, the amount represents a quantityof a frequency modulation parameter and the value represents anotherquantity of the frequency modulation parameter.

FIG. 1B-1 is an embodiment of a table 130 to illustrate that the valuesΓ11, Γ21 through Γn1 of the voltage reflection coefficient aredetermined based on complex voltage and current that is obtained atperiodic time intervals, such as every 0.1 microsecond (μs) or every 0.2μs, over a cycle of operation of the X kilohertz RF generator 112 (FIG.1). For example, the value Γ11 is calculated by the processor 126(FIG. 1) from the complex voltage and current that is measured at 0.1 μsafter a positive crossing during a cycle of the RF signal 130 (FIG. 1)and the value Γ12 is calculated by the processor 126 (FIG. 1) from thecomplex voltage and current that is measured at 0.2 μs after thepositive crossing during the cycle of the RF signal 130. Similarly, thevalue Γn1 corresponds to the complex voltage and current measured at .nmicroseconds after the positive crossing of the cycle of the RF signal130.

In one embodiment, each the values Γ11, Γ21 through Γn1 is an averagecalculated by the processor 126 over a set of multiple cycles of the RFsignal 130. For example, the processor 126 calculates multiple valuesΓ11A, Γ21A through Γn1A of the voltage reflection coefficient from thecomplex voltage and current measured at the output O2 in the same mannerin which the values Γ11, Γ21 through Γn1 are calculated. The value Fl1Ais calculated from the complex voltage and current that is measured at0.1 μs from a time at which a first cycle of the RF signal 130 begins,the value Γ21A is calculated from the complex voltage and current thatis measured at 0.1 μs from a time at which a second cycle of the RFsignal 130 begins, and so on until the value Γn1A is calculated. Thesecond cycle of the RF signal 130 is consecutive to the first cycle ofthe RF signal 130. The processor 126 calculates the value Γ11 as anaverage of the values Γ11A, Γ21A through Γn1A. Similarly, the value Γn1is an average of multiple values of the voltage reflection coefficientand the values of the voltage reflection coefficient are calculated fromthe complex voltage and current measured at .n μs from a time at whicheach corresponding cycle of the RF signal 130 begins.

In one embodiment, instead of calculating the values Γ11, Γ21 throughΓn1 of the voltage reflection coefficient, measured values of thecomplex voltage and current over one cycle of the RF signal 130 are usedby the processor 126.

FIG. 1B-2 is an embodiment of a graph 140 to illustrate a correspondencebetween the values Γ11, Γ21 through Γn1 and time intervals during acycle 1 of the RF signal 130 (FIG. 1). The graph 140 plots a voltagewaveform 142 of the RF signal 130 versus time t. The voltage waveform142 is a sinusoidal or substantially sinusoidal and oscillates overmultiple cycles, such as a cycle 1 and the cycle 2. The cycle 2 isconsecutive to the cycle 1. For example, there are no other cycles ofthe RF signal 130 between the cycles 1 and 2.

The value Γ11 corresponds to a time interval between 0 μs and 0.1 μs. Atthe time of 0.1 μs, the voltage waveform 142 has a positive crossing.Similarly, the value Γ21 corresponds to a time interval between 0.1 and0.2 μs, and so on until the value Γn1 corresponds to a time intervalbetween .(n−1) μs and .n μs.

FIG. 1C is a diagram of an embodiment of an RF path model 150 toillustrate calculation of load impedance values ZL11 through ZLn1 fromthe values Γ11, Γ21 through Γn1 of the voltage reflection coefficient.The RF path model 150 is a computer-based model, which is generated orexecuted or both generated and executed by the processor 126 from atleast a portion of the RF path 102. For example, the RF path model 150includes multiple circuit elements that are connected in the same manneras circuit components of the portion of the RF path 102 or the RF path102. Examples of a circuit element include a capacitor, an inductor, anda resistor. Any two adjacent circuit elements of the RF path model 102are coupled to each other via a connection in the same manner in whichthe corresponding two adjacent circuit components of the portion of theRF path 102 are coupled with each other. To illustrate, when twocapacitors of the RF path 102 are coupled in series with each other, twocapacitors of the RF path model 150 are also coupled in series with eachother. Each of the two capacitors of the RF path model 150 has the samecapacitance as that of a corresponding one of the two capacitors of theRF path 102 or the two capacitors of the RF path model 150 has the sametotal or combined capacitance as that of a total or combined capacitanceof the two capacitors of the RF path 102. As another illustration, whentwo capacitors of the RF path 102 are coupled in parallel with eachother, two capacitors of the RF path model 150 are also coupled inparallel with each other and the two capacitors of the RF path model 150has the same total or combined capacitance as that of a total orcombined capacitance of the two capacitors of the RF path 102.

As yet another illustration, the RF path model 150 has the sameimpedance or substantially the same impedance as a combined impedance ofthe circuit components of the portion of the RF path 102 or of the RFpath 102. The RF path model 150 has substantially the same impedance asthe combined impedance of the circuit components of the portion of theRF path 102 when the impedance of the RF path model 150 is within apredetermined range from the combined impedance. The predetermined rangeis stored in the memory device 128 and accessed by the processor 126. Asan example, the RF path model 150 is received via an input device by theprocessor 126 and is executed by the processor 126. The RF path model150 is created by a user who operates the input device 150. The RF pathmodel 150 is created by the user by using a computer program that isexecuted by the processor 126. As another example, the RF path model 150is generated by the processor 126 and is executed by the processor 126.As another example, the RF path model 150 includes a number of modulesand each module includes one or more resistors, or one or morecapacitors, or one or more inductors, or a combination thereof. As anillustration, each module is expressed as an equation that includes aresistance and a reactance.

Examples of the portion of the RF path 102 include the RF cable RFC2(FIG. 1), or the branch of the impedance matching network 110 (FIG. 1)that is coupled between the input I2 (FIG. 1) of the impedance matchingnetwork 110 and the output of the impedance matching network 110, or theRF transmission line RFT1 (FIG. 1), or the plasma excitation electrode104 (FIG. 1). Additional examples of the portion of the RF path 102include a combination of the RF cable RFC2 and the branch of theimpedance matching network 110 that is coupled between the input I2 ofthe impedance matching network 110 and the output of the impedancematching network 110, or a combination of the RF cable RFC2 and thebranch of the impedance matching network 110 and the RF transmissionline RFT1, or a combination of the RF cable RFC2 and the branch of theimpedance matching network 110 and the RF transmission line RFT1 and theplasma excitation electrode 104.

The processor 126 provides the values Γ11, Γ21 through Γn1 to an inputIn of the RF path model 150 to generate the load impedance values ZL11through ZLn1 at an output Out of the RF path model 150. For example, theprocessor 126 forward propagates the value Γ11 from the input In via thecircuit elements of the RF path model 150 to generate the load impedancevalue ZL11 at the output Out. Before and during the forward propagation,the RF path model 150 is initialized to have a capacitance Cknown1 and aradio frequency RFknown. The capacitance Cknown1 is a capacitance of acapacitor of the branch of the impedance matching network 110 betweenthe input I2 and the output of the impedance matching network 110 duringprocessing of the substrate S (FIG. 1A) and the radio frequency RFknownis a frequency of operation of the Y megahertz RF generator 114 (FIG.1A). To illustrate, the radio frequency RFknown is a frequency ofoperation the Y megahertz RF generator 114. The Y megahertz RF generator114, as an example, operates between 57 MHz and 63 MHz. To furtherillustrate, the frequency RFknown is different for each time interval,such as the time interval between 0 and 0.1 μs, the time intervalbetween 0.1 μs and 0.2 μs, etc. The values Cknown1 and RFknown areprovided as inputs to the processor 134 by the user via the input devicethat is connected to the processor 126 via an input/output interface,e.g., a serial interface, a parallel interface, a universal serial bus(USB) interface, etc. Examples of the input device include a mouse, akeyboard, a stylus, a keypad, a button, and a touch screen.

Continuing with the example, the processor 126 determines impedancevalues Z11, Z21 through Zn1 at the input In of the RF path model 150from the values Γ11, Γ21 through Γn1. To illustrate, the processor 126accesses from the memory device 128 a correspondence, such as a mappingor a one-to-one relationship, between the impedance value Z11 and thevalue Γ11 to identify the impedance values Z11. In a similar manner,impedance values Z21 through Zn1 at the input In of the RF path model150 are determined by the processor 126 from the values Γ21 through Γn1.

Continuing further with the example, the processor 126 propagates theimpedance value Z11 via the circuit elements of the RF path model 150 tocalculate the value ZL11 at the output Out of the RF path model 150. Toillustrate, the processor 126 calculates a directional sum of the valueZ11 and values of the impedances of the circuit elements of the RF pathmodel 150 to calculate the load impedance value ZL11 at the output Outof the RF path model 150. The values of the impedance of the circuitelements are stored in the memory device 128. In a similar manner, theprocessor 126 determines the load impedance values ZL21 through ZLn1 atthe output Out of the RF path model 150 from the impedance values Z21through Zn1 at the input In of the RF path model 150.

In one embodiment, instead of receiving the values Γ11, Γ21 through Γn1of the voltage reflection coefficient at the input In of the RF pathmodel 150, values of a complex voltage and current are received at theinput In by the RF path model 150 from the sensor 131 and the fast dataacquisition device 123 (FIG. 1A) coupled to the output of the Y MHz RFgenerator 114 (FIG. 1A). In this embodiment, there is no need for theprocessor 126 to calculate the values Γ11, Γ21 through Γn1 of thevoltage reflection coefficient from the values of the complex voltageand current. The values ZL11 through ZLn1 of the load impedance arecalculated by the processor 126 by propagating via the RF path model 150the values of the complex voltage and current that are measured by thesensor 131 and the fast data acquisition device 123. For example, theprocessor 126 accesses values of impedance or values of complex voltageand current associated with each of the circuit elements of the RF pathmodel 150 from the memory device 128, calculates a directional sum ofeach of the complex voltage and current values at the input In and thevalues of impedance or complex voltage and current associated with thecircuit elements of the RF path model 150 to compute the values ZL11through ZLn1 of the load impedance at the output Out of the RF pathmodel 150.

FIG. 1D-1 is a diagram of an embodiment of the RF path model 150 toillustrate a determination of operation parameters, which includefrequency parameters or frequency parameters and match networkparameters, based on application of the values ZL11 through ZLn1 of theload impedance at the output of the RF path model 150 to minimize anaverage power reflection coefficient Γ1 avmin ² at the input of the RFpath model 150. For example, the processor 126 is provided an input viathe input device indicating a type of a periodic waveform of the RFsignal 132 that is to be output from the Y MHz RF generator 114 (FIG.1A). To illustrate, the processor 126 is provided an input via the inputdevice and the input includes initial values of the operation parametersdescribed below. The input is provided by the user who is operating theinput device. As another illustration, the operation parameters areprovided by the user as the input and the processor 126 initializesvalues of the operation parameters. The type of periodic waveform or theoperation parameters define a shape of an envelope of the RF signal 132.For example, the type of periodic waveform or the operation parametersprovide a shape of a peak-to-peak amplitude of the RF signal 132.Examples of the type of periodic waveform or the shape of the periodicwaveform include a sinusoidal waveform, a trapezoidal waveform, asawtooth-shaped waveform, a rectangular waveform, and a square-shapedwaveform. In this example, the sinusoidal, the trapezoidal, therectangular, the sawtooth-shaped, and the square-shape are shapes of anenvelope of the RF signal 132. Sometimes, the terms periodic waveformand periodic function are used herein interchangeably. A powerreflection coefficient is another example of the reflection parameter orof the reflection coefficient parameter.

Continuing with the example, the values ZL11 through ZLn1 of the loadimpedance at the output of the RF path model 150 are backpropagated viathe circuit elements of the RF path model 150 to determine multiplevalues ZL1 a through ZLna of load impedance at the input of the RF pathmodel 150. The processor 126 calculates a directional sum of the valueZL11 and of values of impedance of the circuit elements of the RF pathmodel to determine the value ZL1 a and calculates a directional sum ofthe value ZL21 and of the values of impedance of the circuit elements ofthe RF path model 150 to determine the value ZL2 a. In a similar manner,the value ZLna is determined by the processor 126 from the value ZLn1.

Continuing with the example, the processor 126 determines values Γ1 a ²through Γna² of a power reflection coefficient at the input of the RFpath model 150 from the values ZL1 a through ZLna of the load impedanceat the input of the RF path model 150. For example, the processor 126accesses from the memory device 126 a correspondence, such as a mappingor a linking, between the values Γ1 a through Γna of the voltagereflection coefficient and the values ZL1 a through ZLna of the loadimpedance to identify or determine the values Γ1 a through Γna of thevoltage reflection coefficient. To illustrate, the memory device 126stores a correspondence between the value Γ1 a and the value ZL1 a andstores another correspondence between the value Γna and the value ZLna.

Continuing further with the example, the processor 126 calculatessquares of each of the values Γ1 a through Γna of the voltage reflectioncoefficient at the input of the RF path model 150 to determine values Γ1a ² through Γna² of the power reflection coefficient at the input In ofthe RF path model 150. The processor 126 further calculates an averageof the values Γ1 a ² through Γna² of the power reflection coefficient togenerate a first average value ΓAavmin². The processor 126 determinesvalues, such as yMHzavfreqA, yMHzfreqvariationA, thighA, tlowA,ϕrelativeA, and CA, of the operation parameters for which the firstaverage value ΓAavmin² is calculated, where yMHzavfreqA is an averagefrequency of operation at which the Y megahertz RF generator 114 is tobe operated, yMHzfreqvariationA is a variation in the average frequency,thighA is a high dwell time for which a power level or a voltage levelof the Y megahertz RF generator 114 is to remain at a high level, tlowAis a low dwell time for which a power level or a voltage level of the Ymegahertz RF generator 114 is to remain at a low level, ϕprelativeA is arelative phase of the RF signal 132 (FIG. 1A) to be output by the Ymegahertz RF generator 114 compared to the phase of the RF signal 130(FIG. 1A) output by the X kilohertz RF generator 112, and CA is a totalcapacitance to be applied to the branch of the impedance matchingnetwork 110 (FIG. 1A) that is coupled between the input I2 of theimpedance matching network 110 and the output of the impedance matchingnetwork 110. The low level is a voltage or power level that is lowerthan a voltage or power level corresponding to the high level. The highlevel is sometimes referred to herein as a high state and the low levelis sometimes referred to herein as a low state. Also, the low level is abottom envelope or a bottom boundary of multiple values of an RF signaland the high level is a top envelope or a top boundary of multiplevalues of the RF signal. The RF signal oscillates between the low leveland the high level.

To illustrate the determination of the values, such as yMHzavfreqA,yMHzfreqvariationA, thighA, tlowA, ϕrelativeA, and CA, of the operationparameters, the processor 126 provides the values of the operationparameters to the RF path model 150. By providing the values to the RFpath model 150, the processor 126 makes the values available to the RFpath model 150. Once the RF path model 150 has received the values ofthe operation parameters from the processor 126 to be characterized bythe values, the processor 126 backpropagates the values ZL11 throughZLn1 of the load impedance at the output of the RF path model 150 todetermine the values Γ1 a through Γna of the voltage reflectioncoefficient at the input of the RF path model 150. The processor 126accesses the values of the operation parameters from the memory device126 and makes the values available to, e.g., provides the values to, theRF path model 150 for which the values Γ1 a through Γna of the voltagereflection coefficient are determined.

Continuing with the example, the values ZL11 through ZLn1 of the loadimpedance at the output of the RF path model 150 are backpropagated viathe circuit elements of the RF path model 150 to determine multiplevalues ZL1 x through ZLnx of load impedance at the input of the RF pathmodel 150. The processor 126 calculates a directional sum of the valueZL11 and of values of impedance of the circuit elements of the RF pathmodel 150 to determine the value ZL1 x and calculates a directional sumof the value ZL21 and of values of impedance of the circuit elements ofthe RF path model 150 to determine the value ZL2 x. In a similar manner,the value ZLnx is determined by the processor 126 from the value ZLn1.

Continuing with the example, the processor 126 calculates values Γ11 ²through Γn1 ² of a power reflection coefficient at the input of the RFpath model 150 from the values ZL1 x through ZLnx of load impedance atthe input of the RF path model 150. For example, the processor 126accesses from the memory device 126 a correspondence, such as a mappingor a linking, between the values Γ11 through Γn1 of the voltagereflection coefficient and the values ZL1 x through ZLnx of the loadimpedance to identify or determine the values Γ11 through Γn1 of thevoltage reflection coefficient. To illustrate, the memory device 126stores a correspondence between the value Γ11 and the value ZL1 x andstores another correspondence between the value Γn1 and the values ZLnx.

Continuing further with the example, the processor 126 calculatessquares of each of the values Γ11 through Γn1 of the voltage reflectioncoefficient at the input of the RF path model 150 to determine valuesΓ11 ² through Γn1 ² of the power reflection coefficient at the input ofthe RF path model 150. The processor 126 further calculates an averageof the values Γ11 ² through Γn1 ² of the power reflection coefficient togenerate a second average value Γ1 avmin ².

The processor 126 determines values, such as yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1, of the operationparameters for which the first average value Γ1 avmin ² is calculated,where yMHzavfreq1 is an average frequency of operation at which the Ymegahertz RF generator 114 is to be operated, yMHzfreqvariation1 is avariation in the average frequency, thigh1 is a high dwell time forwhich a power level or a voltage level of the Y megahertz RF generator114 is to remain at a high level, tlow1 is a low dwell time for which apower level or a voltage level of the Y megahertz RF generator 114 is toremain at a low level, ϕrelative1 is a relative phase of the RF signal132 (FIG. 1A) to be output by the Y megahertz RF generator 114 comparedto the phase of the RF signal 130 (FIG. 1A) output by the X kilohertz RFgenerator 112, and C1 is a total, such as combined, capacitance of thebranch of the impedance matching network 110 (FIG. 1A) between the inputI2 (FIG. 1A) of the impedance matching network 110 and the output of theimpedance matching network 110. To illustrate the determination of thevalues, such as yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1, and C1, of the operation parameters, the processor 126provides the values of the operation parameters to the RF path model150. By providing the values to the RF path model 150, the processor 126makes the values available to the RF path model 150. Once the RF pathmodel 150 has received the values of the operation parameters from theprocessor 126 to be characterized by the values, the processor 126backpropagates the values ZL11 through ZLn1 of the load impedance at theoutput of the RF path model 150 to determine the values Γ11 through Γn1of the voltage reflection coefficient at the input of the RF path model150. The processor 126 accesses the values of the operation parametersfrom the memory device 126 and makes the values available to, e.g.,provides the values to, the RF path model 150 for which the values Γ11through Γn1 of the voltage reflection coefficient are determined.

The processor 126 determines that the second average value Γ1 avmin ² ofpower reflection coefficient at the input of the RF path model 150 isless than or lower than the first average value ΓAavmin² of the powerreflection coefficient at the input of the RF path model 150. Inresponse to the determination, the processor 126 determines to apply thefrequency parameters yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1 instead of applying the yMHzavfreqA, yMHzfreqvariationA,thighA, tlowA, ϕrelativeA to the Y megahertz RF generator 114 anddetermines to apply the match network parameter C1 instead of applyingthe match network parameter CA to the impedance matching network 110.Once the processor 126 determines the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1, the processor 126updates the initial values of the operation parameters with thedetermined values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1, and C1 of the operation parameters.

The determined values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1, and C1 of the operation parameters are applied during a nextset of one or more cycles of operation of the X kilohertz RF generator112 and the next set is subsequent to, such as follows, a set of one ormore cycles of operation of the X kilohertz RF generator 112 for whichthe operation parameters to be applied are determined by the processor126. For example, the processor 126 receives the complex voltage andcurrent measured at the output O2 (FIG. 1A) of the Y megahertz RFgenerator 114 for 10 cycles of operation of the X kilohertz RF generator112, determines the operation parameters from the complex voltage andcurrent, and applies the operation parameters to the Y MHz RF generator114 during the subsequent 10 cycles of operation of the X kilohertz RFgenerator 112. The subsequent 10 cycles occur after an amount of timetaken by the processor 126 to determine the operation parameters. Anexample of the amount of time includes a portion of the 10 cycles ofoperation of the X kilohertz RF generator 112 and one or more cyclesconsecutive to the 10 cycles of operation of the X kilohertz RFgenerator 112. The one or more consecutive cycles are of operation ofthe X kilohertz RF generator 112. The processor 126 stores the values,such as the values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1, and C1, of the operation parameters in the memory device128.

In one embodiment, the processor 126 repeats the operations or methodsof determining the operation parameters until values of the operationparameters converge to be within a predetermined range. For example,during 10 cycles that are subsequent to the 10 cycles for which thevalues yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, andC1 of the operation parameters are determined, the processor 126controls the Y megahertz RF generator 114 to apply the valuesyMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and controlsone or more variable capacitors of the branch of the impedance matchingnetwork 110 between the input I2 (FIG. 1A) and the output of theimpedance matching network 110 to apply the value C1. During 10 cyclesthat are subsequent to the 10 cycles for which the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 of the operationparameters are applied or during the same 10 cycles during which thevalues yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, andC1 of the operation parameters are applied, the processor 126 determinesvalues yMHzavfreqVAL1, yMHzfreqvariationVAL1, thighVAL1, tlowVAL1,ϕrelativeVAL1, and CVAL1 of the operation parameters in the same mannerin which the values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1,ϕrelative1, and C1 are determined except that the processor 126initiates the RF path model 150 to have a radiofrequency that is adirectional sum of the values yMHzavfreq1 and yMHzfreqvariation1 and tohave the capacitance C1. The processor 126 determines whether the valueyMHzavfreqVAL1 is within a predetermined range from the valueyMHzavfreq1 or that the value yMHzfreqvariationVAL1 is within apredetermined range from the value yMHzfreqvariation1 and so on for theremaining values thighVAL1, tlowVAL1, ϕrelativeVAL1, and CVAL1 andthigh1, tlow1, ϕrelative1, and C1. Upon determining that the valueyMHzavfreqVAL1 is within the predetermined range from the valueyMHzavfreq1 and that the value yMHzfreqvariationVAL1 is within thepredetermined range from the value yMHzfreqvariation1 and so on for theremaining values thighVAL1, tlowVAL1, ϕrelativeVAL1, and CVAL1 andthigh1, tlow1, ϕrelative1, and C1, the processor 126 determinesconvergence of the values of the operations parameters, and does notfurther determine values of the operation parameters.

Continuing with the embodiment, on the other hand, upon determining thatthe value yMHzavfreqVAL1 is not within the predetermined range from thevalue yMHzavfreq1 or that the value yMHzfreqvariationVAL1 is not withinthe predetermined range from the value yMHzfreqvariation1 and so on forthe remaining values thighVAL1, tlowVAL1, ϕrelativeVAL1, and CVAL1 andthigh1, tlow1, ϕrelative1, and C1, the processor 126 continues to applythe operations and methods to determine further values of the operationparameters during further cycles of operation of the X kilohertz RFgenerator 112. The processor 126 applies the values yMHzavfreqVAL1,yMHzfreqvariationVAL1, thighVAL1, tlowVAL1, ϕrelativeVAL1, and CVAL1during the next 10 cycles that are subsequent to the 10 cycles for whichthe values yMHzavfreqVAL1, yMHzfreqvariationVAL1, thighVAL1, tlowVAL1,ϕrelativeVAL1, and CVAL1 are determined in the same manner in which theprocessor 126 applies the values yMHzavfreq1, yMHzfreqvariation1,thigh1, tlow1, ϕrelative1, and C1 of the operation parameters, asdescribed below with reference to FIG. 1D-3.

It should be noted that the values yMHzavfreq1, yMHzfreqvariation1,thigh1, tlow1, ϕrelative1 of the operation parameters are for thetrapezoidal waveform. In one embodiment, different types of values arecalculated for another type of waveform that is to be output by a Ymegahertz RF generator, described herein, after applying the methodsdescribed herein. For example, when the type of waveform is sinusoidal,the operation parameters include an average frequency, a frequencyvariation, such as a frequency amplitude, from the average frequency, aperiod that is the same as that of an RF signal generated by an X kHz RFgenerator described herein, and a phase relative to a phase of the RFsignal generated by the X kHz RF generator. As another example, when thetype of waveform is rectangular, the operation parameters include a highfrequency value, a high frequency time for which the high frequencyvalue is maintained, a low frequency value, a low frequency time forwhich the low frequency value is maintained, a period that is the sameas that of an RF signal generated by an X kHz RF generator describedherein, and a phase relative to a phase of the RF signal generated bythe X kHz RF generator. The high frequency value is greater than the lowfrequency value. As yet another example, when the type of waveform istriangular, the operation parameters include a high frequency value, alow frequency value, a first ramp rate or a first ramp time between thehigh frequency value and the low frequency value, a second ramp rate ora second ramp time between the low frequency value and the highfrequency value, a period that is the same as that of an RF signalgenerated by an X kHz RF generator described herein, and a phaserelative to a phase of the RF signal generated by the X kHz RFgenerator. The high frequency value is greater than the low frequencyvalue. The first ramp rate is lower than, the same as, or greater thanthe second rate.

In one embodiment, the match network parameter C1 is not determined bythe processor 126 and the determination of the match network parameterC1 is optional.

In an embodiment, the terms frequency parameters and frequencymodulation parameters are used herein interchangeably.

FIG. 1D-2 is an embodiment of a graph 170 to illustrate multiple cyclesof an RF signal 172 that is generated by an X kilohertz RF generator,described herein. For example, the RF signal 172 is an example of the RFsignal 130 of FIG. 1A. The graph 170 plots a voltage of the RF signal172 versus time t. The RF signal 172 is a voltage waveform representinga voltage that is output by the X kilohertz RF generator. The RF signal172 is sinusoidal or substantially sinusoidal and oscillates betweenpositive and negative values of voltage in a periodic manner Forexample, the RF signal 172 has a positive crossing PC1, which is a timeat which values of the voltage waveform become positive from negative.Similarly, after a time period, the RF signal 172 has another positivecrossing PC2, which is another time at which values of the voltagewaveform become positive from negative.

A cycle 1 of the RF signal 172 represents a time period of occurrence ofthe voltage waveform. Another cycle 2 of the RF signal 172 representsanother instance of the time period of occurrence of the voltagewaveform. The cycle 2 is consecutive to the cycle 1. For example, thereare no cycles between the cycles 1 and 2. Also, additional cycles 3through (m−1) of the RF signal 172 follow the cycle 2. The cycle 3 isconsecutive to the cycle 2. The cycles 1 through (m−1) form a set 1 ofcycles of the RF signal 172, where m is an integer greater than two.

Moreover, cycles m, (m+1), and so on until (m+q) form a set 2 of cyclesof the RF signal 172, where q is an integer greater than one. The set 2is consecutive to the set 1. For example, there is no set of cyclesbetween the sets 1 and 2. The number of cycles from m through (m+q) ofthe same as the number of cycles from 1 through (m−1) of the set 1. Asan example, the ten cycles described above during which the complexvoltage and current is measured at the output O2 of the Y megahertz RFgenerator 114 (FIG. 1A) to determine the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 of the operationparameters is an example of the cycles 1 through (m−1) of the set 1.Also, the following 10 cycles described above during which the valuesyMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 ofthe operation parameters are applied is an example of the cycles mthrough (m+q) of the set 2.

In one embodiment, instead of the voltage waveform, a power waveform ofthe RF signal 172 is used.

FIG. 1D-3 is a diagram of an embodiment of a system 180, such as aplasma tool, to apply the values yMHzavfreq1, yMHzfreqvariation1,thigh1, tlow1, ϕrelative1, and C1 of the operation parameters during theset 2 of cycles of operation of the X kilohertz RF generator 112 duringprocessing of the substrate S. The system 180 is the same as the system100 in structure and function except that the system 180 excludes thefast data acquisition device 123, the sensor 131 and the fast dataacquisition device 121, and includes a voltage sensor 182, a comparator184, a motor system 186 and a driver system 188. An example of thecomparator 184 includes a processor or an application specificintegrated circuit or a programmable logic device. An example of themotor system 186 includes one or more electric motors, and each electricmotor has a stator and a rotor. An example of the driver system 188includes one or more transistors that are coupled to each other tooutput one or more current signals upon receiving one or more signalsfrom the motor system 186. The comparator 184 is coupled to the voltagesensor 182 and is also coupled to the processor 126. The voltage sensor182 is coupled to the output O1 of the X kilohertz RF generator 112.

The driver system 188 is coupled to the processor 126, and the motorsystem 186 is coupled to the driver system 188. The motor system 186 iscoupled to the one or more circuit components of the impedance matchingnetwork 110 via corresponding one or more connection components. Anexample of each connection component includes one or more rods, or acombination of one or more rods and one or more gears.

The RF signal 130 is generated by the X kilohertz RF generator 112 in amanner similar to that described above with reference to FIG. 1A andsent via the output O1 of the X kilohertz RF generator 112 and the RFcable RFC 1 to the input I1 of the impedance matching network 110. Forexample, the set 2 of cycles of the RF signal 130 is output from the Xkilohertz RF generator 112. The voltage sensor 182 measures a voltage ofthe RF signal 130 at the output O1 of the X kilohertz RF generator 112.The comparator 184 compares the voltage measured by the voltage sensor182 with a value of zero to output comparison results and provides thecomparison results to the processor 126. The comparison results providewhether the voltage is above or below zero or at zero, such as forexample whether the voltage is positive or negative or zero. Theprocessor 126 determines from the comparison results multiple times ormultiple instances at which the voltage is zero and is about to becomepositive from being negative. Based on the multiple times or multipleinstances that are determined by the processor 126, the phase of the RFsignal 130 is determined by the processor 126.

Moreover, the processor 126 accesses the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1 of the frequencyparameters from the memory device 128 and provides the values to the RFpower supply 124. The relative phase ϕrelative1 is determined by theprocessor 126 from the phase of the RF signal 130 that is determinedduring processing of the substrate S. Upon receiving the frequencyparameters, the RF power supply 124 generates an RF signal 190 havingthe values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, andϕrelative1. For example, the RF signal 190 has an envelope or apeak-to-peak amplitude that is of a trapezoidal shape or a pulse shapeor a square wave shape or a sinusoidal shape. The relative phaseϕrelative1 of the RF signal 190 is relative to, such as lags, the phaseof the RF signal 130 that is determined using the voltage sensor 182,the comparator 184 and the processor 126. The RF signal 190 is itself asinusoidal signal or a substantially sinusoidal signal. The RF signal190 is supplied by the RF power supply 124 via the output O2 and the RFcable RFC 2 to the input I2 of the impedance matching network 110.

Moreover, the processor 126 accesses the value C1 from the memory device128, generates an instruction signal, and sends the instruction signalto the driver system 188. An example of the instruction signal is onethat includes one or more amounts of current to be output by the driversystem 188 to control the motor system 186 to achieve a combinedcapacitance of a branch of the impedance matching network 110 betweenthe input I2 and the output of the impedance matching network 110. Uponreceiving the instruction signal, the driver system 186 generates one ormore current signals and sends the current signals to the motor system186.

The motor system 186 is operated according to the one or more currentsignals and controls one or more variable capacitors of the branchbetween the input I2 and the output of the impedance matching network110 to achieve the capacitance C1 of the branch of the impedancematching network 110. For example, a motor of the motor system 186operates to rotate or move in a linear direction a plate of a variablecapacitor in the impedance matching network 110 to change a distance oran area between the plate and another plate of the capacitor to change acapacitance of the capacitor to achieve the capacitance C1 of the branchbetween the input I2 and the output of the impedance matching network110.

The impedance matching network 110, which has the capacitance C1,receives the RF signals 130 and 190, and processes the RF signals 130and 190 in the manner described above with respect to the RF signals 130and 132 (FIG. 1A) to output a modified RF signal 192. For example, theimpedance matching network 110 matches an impedance of the load that iscoupled to the output of impedance matching network 110 with that of thesource that is coupled to the inputs I1 and I2 of the impedance matchingnetwork 110 to output the modified RF signal 192. When one or moreprocess gases are supplied to the gap between the upper electrode 106and the lower electrode of the plasma excitation electrode 104, and thelower electrode of the plasma excitation electrode 104 receives themodified RF signal 192 via the RF transmission line RFT1 from the outputof impedance matching network 110, plasma is stricken or maintainedwithin the plasma chamber 108 to process the substrate S during the set2 of cycles of operation of the X kilohertz RF generator 112. An exampleof a process gas includes an oxygen-containing gas, such as O₂. Otherexamples of a process gas include a fluorine-containing gas, e.g.,tetrafluoromethane (CF₄), sulfur hexafluoride (SF₆), hexafluoroethane(C₂F₆), etc.

In one embodiment, the comparator 184 is a portion of the processor 126and functions described herein as being performed by the comparator 184are performed by the processor 126.

In the embodiment in which the capacitance C1 is not determined, theprocessor 126 does not control the impedance matching network 110 toachieve the capacitance C1.

In one embodiment, the sensor 120 (FIG. 1A) is decoupled from the outputO1 of the X kilohertz RF generator 112 after the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 of the operationparameters are determined or are determined after convergence by theprocessor 126. Also, the sensor 131 is decoupled from the output O2 ofthe Y megahertz RF generator 114.

FIG. 2A is an embodiment of a graph 200 to illustrate a cycle ofoperation of an RF signal 202. The RF signal 202 is an example of the RFsignal 130 of FIG. 1A. The graph 200 plots a voltage of the RF signal130 versus the time tin microseconds.

FIG. 2B is an embodiment of a graph 206 to illustrate a forward voltagewaveform 208 of an RF signal that is supplied by a Y MHz RF generator,described herein. For example, the forward voltage waveform 208 is anexample of a forward voltage of the RF signal 132 of FIG. 1A. The graph206 plots a forward voltage or voltage supplied at an output of the YMHz RF generator versus the time tin microseconds during one cycle ofthe RF signal 202 (FIG. 2A). It should be noted that the forward voltagewaveform 208 has multiple cycles during one cycle of the RF signal 202that is supplied by the X kilohertz RF generator, described above withreference to FIG. 2A.

FIG. 2C is an embodiment of a graph 210 to illustrate a reverse voltagewaveform 212 of an RF signal that is supplied by the Y MHz RF generator,described herein. For example, the reverse voltage waveform 212 is anexample of a reverse voltage of the RF signal 132 of FIG. 1A. The graph210 plots a reverse voltage or voltage reflected towards an output ofthe RF generator versus the time tin microseconds during one cycle ofthe RF signal 202 (FIG. 2A). It should be noted that the reverse voltagewaveform 212 has multiple cycles during one cycle of the RF signal 202that is supplied by the X kilohertz RF generator, described above withreference to FIG. 2A.

From the forward voltage waveform 208 of FIG. 2B and the reverse voltagewaveform 212 of FIG. 2C, it is illustrated that a voltage reflectioncoefficient is a complex number having an amplitude and phase. Theforward voltage has similar peak-to-peak amplitudes or a substantiallyconstant envelope. A peak-to-peak amplitude or an envelope of thereverse voltage becomes low periodically and becomes high periodically.The forward voltage and the reverse voltage together create the complexnumber of the voltage reflection coefficient. A complex number includesan amplitude and a phase.

FIG. 2D is a diagram of an embodiment of a graph 214 to illustrate theforward voltage waveform 208 and the reverse voltage waveform 212 in onegraph. Again, the forward voltage waveform 208 and a change in thepeak-to-peak amplitude of the reverse voltage waveform 212 create thecomplex number of the voltage reflection coefficient.

FIG. 2E is an embodiment of a Smith chart 220 to illustrate values of avoltage reflection coefficient at an output of a Y MHz RF generator,described herein. For example, the Smith chart 220 illustrate values ofthe voltage reflection coefficient at the output O2 of the Y MHz RFgenerator 114 (FIG. 1A) when the methods described herein are notapplied for one cycle of operation of the X kilohertz RF generator 112(FIG. 1A). For example, as shown in FIG. 2E, most values of the voltagereflection coefficient are not close to a center of the Smith chart 220.Accordingly, without applying the methods described herein, a highamount of voltage is reflected towards the Y megahertz RF generator.

FIG. 3A is a diagram of an embodiment of a graph 300 to illustrate acomparison between a frequency of an RF signal that is output from a Ymegahertz RF generator, described herein, after applying the methodsdescribed herein and an RF signal that is output from the Y megahertz RFgenerator before applying the methods. The graph 300 plots a frequency302 of an RF signal and another frequency 304 of another RF signalversus the time tin microseconds. The frequency 302 is of the RF signalthat is output by the Y megahertz RF generator before applying themethods described herein and the frequency 304 is of the RF signal thatis output by the Y megahertz RF generator after applying the method.

The frequency 304 is an example of a frequency of the RF signal 190(FIG. 1D-3) after applying the methods described herein and thefrequency 302 is a frequency of the RF signal 132 before applying themethods. The frequency 302 is a frequency of an envelope or apeak-to-peak amplitude of an RF signal that is output from the Ymegahertz RF generator and the frequency 304 is a frequency of anotherenvelope or a peak-to-peak amplitude of an RF signal output from the Ymegahertz RF generator. As illustrated, the envelope of the RF signalillustrated by the frequency 302 is substantially constant orsubstantially the same. On the other hand, the envelope of the RF signalillustrated by the frequency 304 has a trapezoidal shape.

The graph 300 also illustrates the frequency parameters of the RF signaloutput from the Y megahertz RF generator after applying the methodsdescribed herein. For example, a frequency parameter 306 is an exampleof the value yMHzavfreq1. To illustrate, the frequency parameter 306 isan average frequency of the RF signal 190 during a cycle or a set ofcycles of the X MHz RF generator 112. As another example, a frequencyparameter 308 is an example of the value yMHzfreqvariation1. Toillustrate, the frequency parameter 308 is a value of a variation in apositive direction or a negative direction from the average frequency ofthe RF signal output from the Y megahertz RF generator after applyingthe methods described herein. The positive direction is a direction inwhich voltage values of the RF signal output from the Y megahertz RFgenerator are positive compared to the average frequency yMHzavfreq1 andthe negative direction is a direction in which voltage values of the RFsignal output from the Y megahertz RF generator are negative compared tothe average frequency yMHzavfreq1. As yet another example, a frequencyparameter 310 is an example of the value thigh1. To illustrate, thefrequency parameter 310 is a time period during which a frequency of theRF signal that is output from the Y megahertz RF generator afterapplying the methods described herein is high, such as within apredetermined high range of frequencies. As still another example, afrequency parameter 312 is an example of the value tlow1. To illustrate,the frequency parameter 312 is a time period during which a frequency ofthe RF signal that is output from the Y megahertz RF generator afterapplying the methods described herein is low, such as within apredetermined low range of frequencies.

FIG. 3B is a diagram of an embodiment of a Smith chart 350 to illustratevalues of a voltage reflection coefficient at an output of a Y megahertzRF generator described herein after applying the methods describedherein. For example, the Smith chart 350 illustrate values of thevoltage reflection coefficient at the output O2 of the Y megahertz RFgenerator 114 of FIG. 1D-3 when the RF signal 190 (FIG. 1D-3) isgenerated by the Y megahertz RF generator 114. The Smith chart 350 isplotted for one cycle of operation of an X kilohertz RF generator suchas the X kilohertz RF generator 112 (FIG. 1A), described herein. Asillustrated in FIG. 3B, most of the values of the voltage reflectioncoefficient are closer to a center of the Smith chart 350 compared tovalues of the voltage reflection coefficient illustrated in the Smithchart 220 of FIG. 2E.

FIG. 4A is a diagram of an embodiment of a system 400, such as a plasmatool, to illustrate that the methods described above with respect toFIG. 1A are applicable to the system 400 during recipe developmentinstead of during processing of the substrate S (FIG. 1A). The system400 is the same in structure and function as the system 100 of FIG. 1Aexcept that in the system 400, instead of processing the substrate S, adummy substrate 402 is used for recipe development. For example, thedummy substrate 402 is placed on a top surface of the plasma excitationelectrode 104 in the plasma chamber 108. The X kilohertz RF generator112 generates the RF signal 130 and the Y megahertz RF generator 114generates the RF signal 132. The RF signals 130 and 132 are modified bythe impedance matching network 110 in the manner described above togenerate the modified RF signal 134. The modified RF signal 134 issupplied to the lower electrode embedded in the plasma excitationelectrode 104 to generate plasma in the plasma chamber 108 but there isno processing of the dummy substrate 402. For example, one or moreprocess gases are not supplied to the plasma chamber 108 during recipedevelopment.

The sensor 120 and the fast data acquisition device 121 measure avoltage at the output O1 to generate a voltage waveform, which isanalyzed by the processor 126 in the manner described above withreference to FIG. 1A to determine a phase of the RF signal 130 suppliedby the X kilohertz RF generator 112. Also, the sensor 131 and the fastdata acquisition device 123 measure a complex voltage and current at theoutput O2, which is analyzed by the processor 126 and the mannerdescribed above with reference to FIG. 1A to determine the values Γ11,β21 through Γn1 of a voltage reflection coefficient for one cycle ofoperation of the X kilohertz RF generator 112.

FIG. 4B is a diagram of an embodiment of the table 130, which isgenerated by the processor 126 (FIG. 4A) during recipe development inthe same manner in which the table 130 of FIG. 1B-1 is generated by theprocessor 126 during processing of the substrate S (FIG. 1A). Theprocessor 126 determines the values Γ11, Γ21 through Γn1 of the voltagereflection coefficient for one cycle of operation of the X kilohertz RFgenerator 112 (FIG. 4A) during recipe development.

As described above, in one embodiment, instead of determining each valueΓ11, Γ21 through Γn1 for one cycle of operation of the X kilohertz RFgenerator 112, each value Γ11, Γ21 through Γn1 of the voltage reflectioncoefficient is an average of values of the voltage reflectioncoefficient that are determined by the processor 126 from the complexvoltage and current measured at the output O2 during a set of cycles ofoperation of the X kilohertz RF generator 112 during recipe development.

FIG. 4C is a diagram of an embodiment of the RF path model 150 toillustrate generation of the load impedance values ZL11 through ZLn1from the values Γ11, Γ21 through Γn1 of the voltage reflectioncoefficient for or during recipe development. The load impedance valuesZL11 through ZLn1 are generated by the processor 126 (FIG. 4A) in thesame manner described above with respect to FIG. 1C from the values Γ11,Γ21 through Γn1 except that the load impedance values are generatedduring recipe development instead of during processing of the substrateS (FIG. 1A).

FIG. 4D is a diagram of an embodiment to illustrate a determination ofthe values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1,and C1 of the operation parameters for or during recipe development. Thevalues yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, andC1 of the operation parameters for or during recipe development aredetermined in the same manner as that described above with reference toFIG. 1D-1 for which the average power reflection coefficient inminimized

In one embodiment, the processor 126 determines the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 of the operationparameters for or during recipe development to minimize both the averagepower reflection coefficient and an average voltage reflectioncoefficient. For example, the processor 126 determines the values Γ1 athrough Γna of the voltage reflection coefficient and the values Γ1 a ²through Γna² of the power reflection coefficient at the input of the RFpath model 150 from the values ZL11 through ZLn1 of load impedance atthe output of the RF path model 150 in the same manner as that describedabove with reference to FIG. 1D-1. Before determining the values Γ1 athrough Γna of the voltage reflection coefficient and the values Γ1 a ²through Γna² of the power reflection coefficient, the RF path model 150is initialized by the processor 126 to have the capacitance Cknown1 andthe radio frequency RFknown. The capacitance Cknown1 is a capacitance ofa capacitor of the branch of the impedance matching network 110 betweenthe input I2 of the impedance matching network and the output of theimpedance matching network 110 and the radio frequency RFknown is avalue at which the Y megahertz RF generator 114 is being operated duringrecipe development.

The processor 126 further calculates the average of the values Γ1 a ²through Γna² of the power reflection coefficient at the input of the RFpath model 150 to generate the first average value ΓAavmin² of the powerreflection coefficient. Also, the processor 126 calculates the anaverage of the values Γ1 a through Γna of the voltage reflectioncoefficient at the input of the RF path model 150 to generate a firstaverage value ΓAavmin of the voltage reflection coefficient Theprocessor 126 determines values, such as yMHzavfreqA,yMHzfreqvariationA, thighA, tlowA, ϕrelativeA, and CA, of the operationparameters for which the first average values ΓAavmin² and ΓAavmin arecalculated, where yMHzavfreqA is an average frequency of operation atwhich a Y megahertz RF generator (FIG. 4E) is to be operated duringprocessing of a substrate, yMHzfreqvariationA is a variation in theaverage frequency, thighA is a high dwell time for which a power levelor a voltage level of the Y megahertz RF generator is to remain at ahigh level, tlowA is a low dwell time for which a power level or avoltage level of the Y megahertz RF generator is to remain at a lowlevel, ϕrelativeA is a relative phase of an RF signal to be output bythe Y megahertz RF generator compared to the phase of an RF signal to beoutput by an X kilohertz RF generator used to process the substrate, andCA is a total capacitance to be applied to a branch of an impedancematching network used to process the substrate. The branch of theimpedance matching network is between an input of the impedance matchingnetwork that is coupled to the Y megahertz RF generator and an output ofthe impedance matching network.

Moreover, the processor 126 determines the values Γ11 ² through Γn1 ² ofthe power reflection coefficient and the values Γ11 through Γn1 of thevoltage reflection coefficient at the input of the RF path model 150from the values ZL11 through ZLn1 of load impedance at the output of theRF path model 150 in the same manner as that described above withreference to FIG. 1D-1. Before determining the values Γ11 ² through Γn1² of the power reflection coefficient and the values Γ11 through Γn1 ofthe voltage reflection coefficient, the RF path model 150 is initializedby the processor 126 to have the capacitance Cknown1 and the radiofrequency RFknown.

The processor 126 further calculates the average of the values Γ11 ²through Γn1 ² of the power reflection coefficient to generate the secondaverage value Γ1 avmin ² and also calculates an average of the valuesΓ11 through Γn1 of the voltage reflection coefficient to generate asecond average value Γ1 avmin of the voltage reflection coefficient atthe input of the RF path model 150. The processor 126 determines values,such as yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, andC1, of the operation parameters for which the second average values Γ1avmin ² and Γ1 avmin are calculated, where yMHzavfreq1 is an averagefrequency of operation at which the Y megahertz RF generator is to beoperated to process the substrate, yMHzfreqvariation1 is a variation inthe average frequency, thigh1 is a high dwell time for which a powerlevel or a voltage level of the Y megahertz RF generator is to remain ata high level, tlow1 is a low dwell time for which a power level or avoltage level of the Y megahertz RF generator is to remain at a lowlevel, ϕrelative1 is a relative phase of the RF signal to be output bythe Y megahertz RF generator compared to the phase of the RF signal tobe output by an X kilohertz RF generator to process the substrate, andC1 is a total capacitance to be applied to the branch of the impedancematching network used to process the substrate.

The processor 126 determines that the second average value Γ1 avmin ² ofpower reflection coefficient at the input of the RF path model 150 isless than or lower than the first average value ΓAavmin² of powerreflection coefficient at the input of the RF path model 150 and alsodetermines that the second average value Γ1 avmin of the voltagereflection coefficient at the input of the RF path model 150 is lessthan or lower than the first average value ΓAavmin of voltage reflectioncoefficient at the input of the RF path model 150. In response to thedetermination, the processor 126 determines to apply the frequencyparameters yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1instead of applying the yMHzavfreqA, yMHzfreqvariationA, thighA, tlowA,ϕrelativeA to the Y megahertz RF generator and determines to apply thematch network parameter C1 instead of applying the match networkparameter CA to the impedance matching network used to process thesubstrate. The processor 126 stores the values, such as the valuesyMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1, ofthe operation parameters in the memory device 128 for later access by aprocessor 464 (FIG. 4E) from another memory device 468 (FIG. 4E).

FIG. 4E is a diagram of an embodiment of a system 450, such as a plasmatool, to illustrate application of the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 of the operationparameters that are determined during recipe development. The valuesyMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, ϕrelative1, and C1 ofthe operation parameters are applied during processing of a substrate SUin a plasma chamber 458. As an example, the processing of the substrateSU is done by an entity that performs the recipe development and isperformed after the recipe development. The system 450 includes an Xkilohertz RF generator 452, a Y megahertz RF generator 454, the plasmachamber 458, an impedance matching network 456, a computer 463, a driversystem 470, a motor system 472, a comparator 480, and a voltage sensor482.

The X kilohertz RF generator 452 is similar in structure and function tothat of the X kilohertz RF generator 112 (FIG. 4A) and includes an RFpower supply 474. For example, the X kilohertz RF generator 452 is a 400kHz RF generator. The RF power supply 474 is also similar and structureand function as the RF power supply 122 (FIG. 4A) of the X kilohertz RFgenerator 112. To illustrate, the RF power supply 474 is an RFoscillator.

Similarly, the Y megahertz RF generator 454 is similar in structure andfunction to that of the Y megahertz RF generator 114 (FIG. 4A) andincludes an RF power supply 476. For example, the Y megahertz RFgenerator 454 is a 60 MHz RF generator. The RF power supply 476 is alsosimilar and structure and function as the RF power supply 124 (FIG. 4A)of the Y megahertz RF generator 114. To illustrate, the RF power supply476 is an RF oscillator.

The comparator 480 is similar in structure and function as that of thecomparator 184 of FIG. 1D-3. For example, the comparator 480 may beimplemented as a part of the processor 464 of the computer 463.

The impedance matching network 456 is also similar in structure andfunction as that of the impedance matching network 110 of FIG. 4A. Forexample, a branch of the impedance matching network 456 between an inputI21 of the impedance matching network 456 and an output of the impedancematching network 456 has a combined impedance that is within apredetermined range from a combined impedance of the branch between theinput I2 and the output of the impedance matching network 110. As anexample, a combined impedance, as described herein, of a branch of animpedance matching network is a combination or a sum of impedances ofall electrical components of the branch of the impedance matchingnetwork.

The motor system 472 is similar in structure and function as that of themotor system 186 (FIG. 1D-3) and the driver system 470 is also similarin structure and function as that of the driver system 188 (FIG. 1D-3).For example, the motor system for 72 includes one or more electricmotors and the driver system for 70 includes a network of transistors.

Examples of a computer, such as the computer 463, are provided above.The computer 463 includes a processor 464 and a memory device 468.Examples of a processor, such as the processor 464, are provided above.Examples of a memory device, such as the memory device 468, are providedabove. The processor 464 is coupled to the memory device 468 and is alsocoupled to the RF power supplies 474 and 476.

The plasma chamber 458 includes a plasma excitation electrode 462 and anupper electrode 460, which is coupled to a ground potential. The plasmaexcitation electrode 462 is similar in structure and function as that ofthe plasma excitation electrode 104 of the plasma chamber 108 (FIG. 4A).For example, a lower electrode of the plasma excitation electrode 462 isfabricated from aluminum or an alloy of aluminum. Also, the upperelectrode 460 is similar in structure and function as that of the upperelectrode 106 of FIG. 4A, and is placed above the plasma excitationelectrode 462 to form a gap between the upper electrode 460 and theplasma excitation electrode 462. For example, the upper electrode 460 isfabricated from aluminum or an alloy of aluminum.

The RF power supply 474 of the X kilohertz RF generator 452 is coupledvia an output O11 of the X kilohertz RF generator 452 and an RF cableRFC11 to an input I11 of the impedance matching network 456. In asimilar manner, the RF power supply 476 of the Y megahertz RF generator454 is coupled via an output O21 of the Y megahertz RF generator 454 andan RF cable RFC21 to the input I21 of the impedance matching network456.

The output of the impedance matching network 456 is coupled via an RFtransmission line RFT11 to the lower electrode of the plasma excitationelectrode 462. The processor 464 is coupled to the driver system 470 andthe comparator 480. The driver system 470 is coupled to the motor system472, which is connected to the impedance matching network 456 via one ormore connection components, examples of which are provided above. Thevoltage sensor 482 is coupled to the output O11 of the X kilohertz RFgenerator 452 and is coupled to the comparator 480.

The RF power supply 474 of the X kilohertz RF generator 452 generates anRF signal 484 for one or more cycles, and supplies the RF signal 484 viathe output O11 and the RF cable RFC11 to the input I11 of the impedancematching network 456. The voltage sensor 482 measures a voltage of theRF signal 484 at the output O11 of the X kilohertz RF generator 452. Thecomparator 480 compares the voltage measured by the voltage sensor 482with a value of zero to output comparison results and provides thecomparison results to the processor 464. The comparison results providewhether the voltage is above or below zero or at zero, such as, forexample, whether the voltage is positive or negative or zero. Theprocessor 464 determines from the comparison results multiple times orinstances at which the voltage is zero and is about to become positivefrom being negative. Based on the times or instances that are determinedby the processor 464, a phase of the RF signal 484 is determined by theprocessor 464.

The computer 463 receives the values of the operation parameters fromthe computer 118 of FIG. 4A. For example, the values of the operationparameters are received by the processor 464 of the computer 463 via acomputer network, such as the Internet or an intranet or a combinationthereof, from the processor 126 of the computer 118. The processor 464stores the values, such as the values yMHzavfreq1, yMHzfreqvariation1,thigh1, tlow1, ϕrelative1, and C1, of the operation parameters in thememory device 468 of the computer 463.

Moreover, the processor 464 provides the values yMHzavfreq1,yMHzfreqvariation1, thigh1, tlow1, ϕrelative1 of the frequencyparameters to the RF power supply 476. The relative phase ϕrelative1 isdetermined by the processor 464 from the phase of the RF signal 484 thatis determined during processing of the substrate SU. Upon receiving thefrequency parameters, the RF power supply 476 generates an RF signal 486having the values yMHzavfreq1, yMHzfreqvariation1, thigh1, tlow1, andϕrelative1. For example, the RF signal 486 has an envelope or apeak-to-peak amplitude that is of a trapezoidal shape or a pulse shapeor a square wave shape or a sinusoidal shape. The RF signal 486 isitself a sinusoidal signal or a substantially sinusoidal signal. The RFsignal 486 is supplied by the RF power supply 476 via the output O21 andthe RF cable RFC 21 to the input I21 of the impedance matching network456. The RF signal 486 is generated during the one or more cycles of theRF signal 484.

Moreover, the processor 464 generates an instruction signal and sendsthe instruction signal to the driver system 470. An example of theinstruction signal is one that includes one or more amounts of currentto be output by the driver system 470 to control the motor system 472 toachieve a combined capacitance of the branch between the input I21 andthe output of the impedance matching network 456. Upon receiving theinstruction signal, the driver system 470 generates one or more currentsignals and sends the current signals to the motor system 472.

The motor system 472 is operated according to the one or more currentsignals and controls one or more variable capacitors of the impedancematching network 456 to achieve the capacitance C1 of the impedancematching network 456. For example, a motor of the motor system 472operates to rotate or move in a linear direction a plate of a capacitorin the impedance matching network 456 to change an area or distancebetween the plate and another plate of the capacitor to change acapacitance of the capacitor to achieve the capacitance C1 of theimpedance matching network 456.

The impedance matching network 456, which has the capacitance C1,receives the RF signals 484 and 486, and processes the RF signals 484and 486 in the manner described above with respect to the RF signals 130and 132 (FIG. 4A) to output a modified RF signal 488. For example, theimpedance matching network 456 matches an impedance of a load that iscoupled to the output of impedance matching network 456 with that of asource that is coupled to the inputs I11 and I21 of the impedancematching network 456 to output the modified RF signal 488. An example ofthe load coupled to the output of the impedance matching network 456includes the plasma chamber 458 and the RF transmission line RFT11. Anexample of the source coupled to the inputs I11 and I21 include the Xkilohertz RF generator 452, the Y megahertz RF generator 454, and the RFcables RFC11 and RFC21.

The lower electrode of the plasma excitation electrode 462 receives themodified RF signal 488 via the RF transmission line RFT11 from theoutput of impedance matching network 456. In addition to receiving themodified RF signal 488, the one or more process gases are received bythe plasma chamber 458 to strike or maintain plasma within the plasmachamber 458. The plasma facilitates processing of the substrate SUduring one or more cycles of operation of the X kilohertz RF generator452.

In one embodiment, the method described herein with reference to FIG. 4Eare used to process many substrates within the plasma chamber 458 or areused for a different system that is similar in structure and function asthe system 450.

In one embodiment, instead of an average frequency of a Y megahertz RFgenerator, a baseline frequency is used or determined. Examples of thebaseline frequency include an average frequency and a median frequency.

In an embodiment, during processing of the substrate SU, the processor126 continues to apply the frequency parameters determining duringrecipe development to a baseline frequency of the Y megahertz RFgenerator 454. For example, during processing of the substrate S, thevalues yMHzfreqvariation1, thigh1, tlow1, and ϕrelative1, are applied bythe processor 126 to an average frequency of operation of the Ymegahertz RF generator 454. To illustrate, the processor 126 modifiesthe average frequency of the Y MHz RF generator 454 during theprocessing of the substrate SU by the values yMHzfreqvariation1, thigh1,and tlow1 while achieving a relative phase of ϕrelative1 between the RFsignal 486 generated by the Y MHz RF generator 454 and the RF signal 484generated by the X MHz RF generator 452.

In the embodiment, the baseline frequency of the Y megahertz RFgenerator 454 is determined by the processor 464 by applying one of manymethods. For example, a sensor, such as a complex voltage and currentsensor, is coupled to the output O21 of the Y megahertz RF generator454. The sensor is also coupled to the processor 464. The sensor that iscoupled to the processor 464 measures a complex voltage and current, andprovides the complex voltage and current to the processor 464. Theprocessor 464 calculates or determines, from the complex voltage andcurrent, a power-based parameter, such as an average power reflected ata fundamental operating frequency of the Y megahertz RF generator 454towards the Y megahertz RF generator 454, an average power reflectedtowards the Y megahertz RF generator 454 at fundamental frequencies ofthe X kilohertz RF generator 452 and the Y megahertz RF generator 454including sidebands, an average power reflected towards the Y megahertzRF generator 454 at the fundamental frequencies of the X kilohertz RFgenerator 452 and the Y megahertz RF generator 454 without thesidebands, an average power reflection coefficient, and an average powerreflection coefficient and an average voltage reflection coefficient.The sidebands include harmonic frequencies associated with, e.g.,generated from, based on, etc., the fundamental frequencies of the Xkilohertz RF generator 452 and the Y megahertz RF generator 454. As anexample, the processor 454 accesses a look-up table stored in the memorydevice 468 to determine the power-based parameter from the complexvoltage and current measured by the sensor that is coupled to theprocessor 454.

Continuing with the embodiment, the processor 464 determines whether oneor more values of the determined power-based parameter received from thesensor are within a pre-set range from a power-based parameter valuestored in the memory device 468. Upon determining that the one or morevalues of the determined power-based parameter are not within thepre-set range from the power-based parameter value stored in the memorydevice 468, the processor 464 changes a frequency of operation of the Ymegahertz RF generator 454. The processor 464 continues to the changethe frequency of operation of the Y megahertz RF generator 454 until oneor more values of the determined power-based parameter received from thesensor are within the pre-set range from the power-based parameter valuestored in the memory device 468. The processor 464 determines an averageof values of the frequency of operation of the Y megahertz RF generator454 for which the one or more values of the determined power-basedparameter received from the sensor are within the pre-set range from thepower-based parameter value stored in the memory device 468 to determinethe baseline frequency. As another example, instead of the average ofthe values of the frequency of operation of the Y megahertz RF generator454, a median the values of the frequency of operation of the Ymegahertz RF generator 454 is determined by the processor 468 to be thebaseline frequency. The determination of the average frequency based onthe power-based parameter allows for variations in the baselinefrequency from one plasma tool to another, e.g., from an RF generator ofone plasma tool to an RF generator of another plasma tool. An RFgenerator of a plasma tool operates at a different baseline frequencyfrom an RF generator of another plasma tool. Applying the valuesyMHzfreqvariation1, thigh1, tlow1, and ϕrelative1 to the differentbaseline frequencies of the RF generators of the plasma tools allows fortool-to-tool variation in a baseline frequency.

FIG. 5A is a diagram of an embodiment of a system 500, such as a plasmatool, to illustrate generation of the values Γ11, Γ21 through Γn1 of thevoltage reflection coefficient by the processor 126 during recipedevelopment. The system 500 is the same as the system 100 (FIG. 1A) orthe system 400 (FIG. 4A) except that in the system 500, the values Γ11,Γ21 through Γn1 are determined for each bin or segment or portion of atime period of a cycle of the RF signal 130 that is output by the Xkilohertz RF generator 112. The system 500 has the same structure andthe same function as that of the system 100 or the system 400 exceptthat in the system 500, the value Γ11 is generated from a value ofcomplex voltage and current that is measured by the sensor 131 and thefast data acquisition device 123 during a first bin of the cycle of theRF signal 130, the value Γ12 is generated from a value of complexvoltage and current that is measured by the sensor 131 and the fast dataacquisition device 123 during a second bin of the cycle of the RF signal130, and so on until the value Γn1 is generated from a value of complexvoltage and current that is measured by the sensor 131 and the fast dataacquisition device 123 during an nth bin of the cycle of the RF signal130. The second bin is consecutive to the first bin and a third bin ofthe cycle of the RF signal 130 is consecutive to the second bin and soon until the nth bin is consecutive to an (n−1)th bin of the cycle ofthe RF signal 130. As an example, a time segment of the RF signal 142(FIG. 1B-2) from 0 to 0.1 microseconds is an example of the first bin, atime segment of the RF signal 142 from 0.1 microseconds to 0.2microseconds is an example of the second bin, a time segment of the RFsignal 142 from 0.2 microseconds to 0.3 microseconds is an example ofthe third bin, and a time segment of the RF signal 142 from 0.(n−1)microseconds to 0.n microseconds is an example of the nth bin. Thesystem 500 operates in the same manner as that of the system 100 or 400except that in the system 500, the dummy substrate 402 is being used andthe values Γ11, Γ21 through Γn1 are generated for the bins of the cycleof the RF signal 130. In the system 500, there is no processing of thesubstrate S.

FIG. 5B is a diagram of an embodiment of a table 510 that is generatedby the processor 126 (FIG. 5A) for recipe development. The table 510 isthe same as the table 130 of FIG. 1B-1 or FIG. 4B except that in thetable each of the values Γ11, Γ21 through Γn1 corresponds to a differentbin of the cycle of the RF signal 130 (FIG. 5A). For example, the valueΓ11 is determined by the processor 126 from a value of complex voltageand current that is measured during a bin 1, e.g., the first bin, of thecycle of the RF signal 130 and the value Γ21 is determined by theprocessor 126 based on a value of complex voltage and current that ismeasured during a bin 2, e.g., the second bin, of the cycle of the RFsignal 130. The table 510 is stored by the processor 126 in the memorydevice 128 (FIG. 5A).

In one embodiment, each value Γ11, Γ21 through Γn1 of the voltagereflection coefficient is an average that is calculated by the processor126 for a corresponding bin over multiple cycles of the RF signal 130.For example, the value Γ11 is an average of multiple values of thevoltage reflection coefficient, and each of the multiple values isdetermined by the processor 126 for bin 1 of each corresponding cycle ofthe RF signal 130. To illustrate, the value Γ11 is an average of a firstvalue and a second value. The first value is calculated by the processor126 based on a value of complex voltage and current that is measured bythe sensor 131 and the fast data acquisition device 123 (FIG. 5A) duringa bin 1 of a first cycle of the RF signal 130. Similarly, the secondvalue is calculated by the processor 126 based on a value of complexvoltage and current that is measured by the sensor 131 and the fast dataacquisition device 123 during a bin 1 of a second cycle of the RF signal130. The second cycle is consecutive to the first cycle. Each of thefirst and second cycles is divided into n number of bins from 1 throughn by the processor 126.

FIG. 5C is a diagram of an embodiment of the RF path model 150 toillustrate generation of the load impedance values ZL11 through ZLn1 foreach bin of the cycle of the RF signal 130 (FIG. 5A) from the valuesΓ11, Γ21 through Γn1 of the voltage reflection coefficient during recipedevelopment. For example, the load impedance value ZL11 for the bin 1 isdetermined by the processor 126 from the value Γ11, the load impedancevalue ZL21 for the bin 2 is determined by the processor 126 from thevalue Γ21, and so on until the load impedance value ZLn1 for the bin nis determined by the processor 126 from the value Γn1. It should benoted that the load impedance values ZL11 through ZLn1 for each bin ofthe cycle of the RF signal 130 are determined from the values Γ11, Γ21through Γn1 of the voltage reflection coefficient in the same manner asthat described above with respect to FIG. 1C.

In one embodiment, instead of the values Γ11, Γ21 through Γn1 of thevoltage reflection coefficient, measured values of the complex voltageand current are applied by the processor 126 to determine the loadimpedance values ZL11 through ZLn1 for each bin of the cycle of the RFsignal 130

FIG. 5D is a diagram of an embodiment of the RF path model 150 toillustrate a determination of values of the operation parameters forwhich values of the power reflection coefficient for the bins of thecycle 130 of the RF signal 130 (FIG. 5A) are minimized during recipedevelopment. There is no predetermined waveform or the initial values ofthe operation parameters provided to the processor 126 (FIG. 5A). Forexample, the type of the periodic waveform of the RF signal 132 that isto be output from the Y MHz RF generator 114 is not provided to the RFpath model 150.

Values of the operation parameters for each bin are determined by theprocessor 126 for which a value of the power reflection coefficient atthe input of the RF path model 150 is minimized when a value of the loadimpedance is applied to the output of the RF path model 150. Forexample, the RF path model 150 is initialized to have the capacitanceCknown1 and the radio frequency RFknown. The capacitance Cknown1 is acapacitance of a capacitor of the circuit components of branch of theimpedance matching network 110 between the input I2 and the output ofthe impedance matching network 110 and the radio frequency RFknown is avalue at the Y megahertz RF generator 114 is being operated duringrecipe development. The value ZL11 of the load impedance at the outputof the RF path model 150 is backpropagated via the circuit elements ofthe RF path model 150 to determine the value ZL1 a of load impedance atthe input of the RF path model 150. The processor 126 calculates adirectional sum of the value ZL11 and of values of impedance of thecircuit elements of the RF path model 150 to determine the value ZL1 a.

Continuing with the example, the processor 126 calculates the value Γ1 a² of the power reflection coefficient at the input of the RF path model150 from the value ZL1 a of load impedance at the input of the RF pathmodel 150. For example, the processor 126 accesses from the memorydevice 126 a correspondence, such as a mapping or a linking, between thevalue Γ1 a of the voltage reflection coefficient and the value ZL1 a ofthe load impedance to identify or determine the value Γ1 a of thevoltage reflection coefficient.

Continuing further with the example, the processor 126 calculates asquare of the value Γ1 a of the voltage reflection coefficient at theinput of the RF path model 150 to determine the value Γ1 a ² of thepower reflection coefficient at the input of the RF path model 150. Theprocessor 126 determines values, such as yMHzavfreq1A andyMHzfreqvariation1A, and C1A of the operation parameters for which thevalue Γ1 a ² of the power reflection coefficient is calculated, whereyMHzavfreq1A is an average frequency of operation at which the Ymegahertz RF generator 454 (FIG. 5E) is to be operated during the bin 1of a cycle of an RF signal output from an X KHz RF generator 452 (FIG.5E), yMHzfreqvariation1A is a variation in the average frequencyyMHzavfreq1A during the bin 1, and C1A is a total capacitance to beapplied to a branch between the input I21 and the output of theimpedance matching network 456 (FIG. 5E).

To illustrate the determination of the values, such as yMHzavfreq1A,yMHzfreqvariation1A, and C1A, of the operation parameters, the processor126 provides the values of the operation parameters to the RF path model150. By providing the values to the RF path model 150, the processor 126makes the values available to the RF path model 150. Once the RF pathmodel 150 has received the values of the operation parameters from theprocessor 126 to be characterized by the values, the processor 126backpropagates the value ZL11 of the load impedance at the output of theRF path model 150 to determine the value Γ1 a of the voltage reflectioncoefficient at the input of the RF path model 150. The processor 126accesses the values of the operation parameters from the memory device126 and makes the values available to, e.g., provides the values to, theRF path model 150 for which the value Γ1 a of the voltage reflectioncoefficient is determined.

Continuing with the example, the value ZL11 of the load impedance at theoutput of the RF path model 150 is backpropagated by the processor 126via the circuit elements of the RF path model 150 to determine the valueZL1 x of load impedance at the input of the RF path model 150. Theprocessor 126 calculates a directional sum of the value ZL11 and ofvalues of impedance of the circuit elements of the RF path model todetermine the value ZL1 x.

Continuing with the example, the processor 126 calculates the value Γ11² of the power reflection coefficient at the input of the RF path model150 from the value ZL1 x of load impedance at the input of the RF pathmodel 150. For example, the processor 126 accesses from the memorydevice 126 a correspondence, such as a mapping or a linking, between thevalue Γ11 of the voltage reflection coefficient and the value ZL1 x ofthe load impedance to identify or determine the value Γ11 of the voltagereflection coefficient.

Continuing further with the example, the processor 126 calculates asquare of the value Γ11 of the voltage reflection coefficient at theinput of the RF path model 150 to determine the value Γ11 ² of the powerreflection coefficient at the input of the RF path model 150. Theprocessor 126 determines values, such as yMHzavfreqn1,yMHzfreqvariationn1, and Cn1, of the operation parameters for which thevalue Γ11 ² of the power reflection coefficient is calculated, whereyMHzavfreqn1 is an average frequency of operation at which the Ymegahertz RF generator 454 (FIG. 5E) is to be operated,yMHzfreqvariationn1 is a variation in the average frequency, and Cn1 isa total capacitance to be applied to the branch between the input I21and the output of the impedance matching network 456 (FIG. 5E).

To illustrate the determination of the values, such as yMHzavfreqn1,yMHzfreqvariationn1, and Cn1, of the operation parameters, the processor126 provides the values of the operation parameters to the RF path model150. By providing the values to the RF path model 150, the processor 126makes the values available to the RF path model 150. Once the RF pathmodel 150 has received the values of the operation parameters from theprocessor 126 to be characterized by the values, the processor 126backpropagates the value ZL11 of the load impedance at the output of theRF path model 150 to determine the value Γ11 of the voltage reflectioncoefficient at the input of the RF path model 150. The processor 126accesses the values of the operation parameters from the memory device126 and makes the values available to, e.g., provides the values to, theRF path model 150 for which the value Γ11 of the voltage reflectioncoefficient is determined.

The processor 126 determines that the value Γ11 ² of the powerreflection coefficient at the input of the RF path model 150 is lessthan or lower than the value Γ1 a ² of the power reflection coefficientat the input of the RF path model 150 for the bin 1. In response to thedetermination, the processor 126 determines to apply the frequencyparameters yMHzavfreqn1 and yMHzfreqvariationn1 instead of applying thefrequency parameters yMHzavfreq1A and yMHzfreqvariation1A to the Ymegahertz RF generator 454 (FIG. 5E) and determines to apply the matchnetwork parameter Cn1 instead of applying the match network parameterC1A to the impedance matching network 456 (FIG. 5E).

In a similar manner, values yMHzfreqvariationn2, and Cn1 of theoperation parameters are determined by the processor 126 for the bin 2of the RF signal 484 (FIG. 5E) to be generated by the X kilohertz RFgenerator 452 (FIG. 5E) except that for the bin 2, the processor 126determines the value yMHzavfreqn2 to be a directional sum of the valueyMHzavfreqn1 and the value yMHzfreqvariationn1, which are calculated forthe bin 1. Also, for the bin 2, the processor 126 initiates the RF pathmodel 150 to be at the value yMHzavfreqn2. Also, similarly, valuesyMHzavfreqnn, yMHzfreqvariationnn, and Cn1 are determined by theprocessor 126 for bin n of the RF signal 484 to be generated by the Xkilohertz RF generator 452 (FIG. 5E). The processor 126 stores thevalues, such as the values yMHzavfreqn1, yMHzfreqvariationn1,yMHzfreqvariationn2, yMHzfreqvariationnn, and Cn1, of the operationparameters for the bins 1 through n in the memory device 128.

In one embodiment, the value Cn1 of the match network parameter of theRF path model 150 is determined after determining the values of thefrequency parameters of the RF path model 150 for the bins 1 through n.For example, the processor 126 determines the values yMHzavfreqn1,yMHzfreqvariationn1, yMHzfreqvariationn2, and so on until the valueyMHzfreqvariationnn in a similar manner to that described above withreference to FIG. 5D except that the processor 126 does not determinethe values Cn1 and C1A. After the values yMHzavfreqn1,yMHzfreqvariationn1, yMHzfreqvariationn2, and so on until the valueyMHzfreqvariationnn are determined, the processor 126 determines thevalue Cn1 for which an average of the values of the power reflectioncoefficient at the input of the RF path model 150 is minimum. Toillustrate, the processor 126 calculates a first average of the valuesΓ1 a ², Γ2 a ², and Γna² of the power reflection coefficient at theinput of the RF path model 150 and determines that the RF path model 150has the value C1A to achieve the first average, calculates a secondaverage value Γ1 avmin ² of the values Γ11 ², Γ21 ², and Γn1 ² of thepower reflection coefficient at the input of the RF path model 150 anddetermines that the RF path model 150 has the value Cn1 to achieve thesecond average value Γ1 avmin ². The processor 126 further determinesthat the second average value Γ1 avmin ² is lower than the firstaverage. Upon determining that the second average value Γ1 avmin ² islower than the first average, the processor 126 determines that thevalue Cn1 of the match network parameter for which the second averagevalue Γ1 avmin ² is calculated is to be applied to the impedancematching network 456 of FIG. 5E. The processor 126 stores the valuesyMHzavfreqn1, yMHzfreqvariationn1, yMHzfreqvariationn2, andyMHzfreqvariationnn, and the value Cn1 of the operation parameters inthe memory device 128 (FIG. 5A).

FIG. 5E is a diagram of an embodiment of the system 450 to illustrateuse of the values yMHzavfreqn1, yMHzfreqvariationn1,yMHzfreqvariationn2, and yMHzfreqvariationnn, and the value Cn1 duringprocessing of the substrate SU. In the system 450, the computer 463receives the values of the operation parameters from the computer 118 ofFIG. 5A. For example, the values yMHzavfreqn1, yMHzfreqvariationn1,yMHzfreqvariationn2, and yMHzfreqvariationnn, and the value Cn1 of theoperation parameters are received by the processor 464 of the computer463 via the computer network from the processor 126 of the computer 118.The processor 464 stores the values, such as the values yMHzavfreqn1,yMHzfreqvariationn1, yMHzfreqvariationn2, and yMHzfreqvariationnn, andthe value Cn1, of the operation parameters in the memory device 468 ofthe computer 463.

While processing the substrate SU in the plasma chamber 458, theprocessor 464 in response to determining that the phase of the RF signal484 is such that the RF signal 484 has crossed a zero crossing toachieve a positive voltage or power value from a negative voltage orpower value, sends the values yMHzavfreqn1 and yMHzfreqvariationn1 ofthe frequency parameters for the bin 1 of the RF signal 484 to the RFpower supply 476. Upon receiving the values yMHzavfreqn1 andyMHzfreqvariationn1, the RF power supply 476 generates an RF signal 550having a frequency that is a directional sum of the values yMHzavfreqn1and yMHzfreqvariationn1 during a time period of the bin 1 of a firstcycle of the RF signal 484.

The processor 464 determines that a time period for the bin 2 of thefirst cycle of the RF signal 484 is about to start. Upon determining so,the processor 464 accesses the value yMHzfreqvariationn2 from the memorydevice 468 and provides the value yMHzfreqvariationn2 to the RF powersupply 476. During the time period of the bin 2 of the first cycle ofthe RF signal 484, the RF power supply 476 outputs the RF signal 550having a directional sum of an average value of the frequency parameterand the value yMHzfreqvariationn2 The average value of the frequencyparameter for the bin 2 of the RF signal 484 is a directional sum of thevalues yMHzavfreqn1 and yMHzfreqvariationn1. In a similar manner, theprocessor 464 provides the remaining values of the frequency parametersfor the remaining bins from 3 through n to the RF power supply 476during remaining bins of the first cycle of the RF signal 484 generatedby the X kilohertz RF generator 452 to output the RF signal 550.

During following cycles of RF signal 484, the frequency parameters forthe bins 1 through n of each of the following cycles are the same asthat during bins 1 through n of the first cycle. For example, the RFsignal 550 has the values yMHzavfreqn1 and yMHzfreqvariationn1 duringthe bin 1 of a second cycle of the RF signal 484. The RF signal 550 hasa directional sum of an average value of the frequency parameter and thevalue yMHzfreqvariationn2 during the bin 2 of the second cycle of the RFsignal 484. The average value of the frequency parameter for the bin 2of the second cycle of the RF signal 484 is a directional sum of thevalues yMHzavfreqn1 and yMHzfreqvariationn1.

Moreover, the processor 464 controls a combined capacitance of thebranch between the input I21 and the output of the impedance matchingnetwork 456 by controlling the motor system 472 in the same manner asthat is described above with reference to FIG. 4E. For example, theprocessor 464 controls one or more capacitors of the impedance matchingnetwork 456 via the driver system 470 and the motor system 472 toachieve the capacitance Cn1 of the branch between the input I21 and theoutput of the impedance matching network 456 during processing of thesubstrate SU.

The RF power supply 476 supplies the RF signal 550 via the output O21 ofthe Y megahertz RF generator 454 and the RF cable RFC 21 to the inputI21 of the impedance matching network 456 having the combinedcapacitance Cn1. Upon receiving the RF signals 484 and 550, theimpedance matching network 456 matches an impedance of the load that iscoupled to the output of impedance matching network 456 with that of thesource that is coupled to the inputs I11 and I21 of the impedancematching network 456 to output a modified RF signal 552 at the output ofthe impedance matching network 456. Once the lower electrode of theplasma chamber 458 receives the modified RF signal 552 and the one ormore process gases are supplied to the gap between the upper electrode460 and the lower electrode of the plasma excitation electrode 462 ofthe plasma chamber 458, plasma is stricken or maintained within theplasma chamber 458 to process the substrate SU within the plasma chamber458.

In one embodiment, a directional sum, as used herein, is a vector sum.

In one embodiment, the method described herein with reference to FIG. 5Eare used to process many substrates within the plasma chamber 458 or areused for a different system that is similar in structure and function asthe system 450.

It should be noted that in an embodiment, instead of applying an RFsignal to the lower electrode of the plasma excitation electrode 462 andcoupling the upper electrode 460 to the ground potential, the RF signalis applied to the upper electrode 460 and the lower electrode of theplasma excitation electrode 462 is coupled to the ground potential.

Embodiments, described herein, may be practiced with various computersystem configurations including hand-held hardware units, microprocessorsystems, microprocessor-based or programmable consumer electronics,minicomputers, mainframe computers and the like. The embodiments,described herein, can also be practiced in distributed computingenvironments where tasks are performed by remote processing hardwareunits that are linked through a computer network.

In some embodiments, a controller is part of a system, which may be partof the above-described examples. The system includes semiconductorprocessing equipment, including a processing tool or tools, chamber orchambers, a platform or platforms for processing, and/or specificprocessing components (a wafer pedestal, a gas flow system, etc.). Thesystem is integrated with electronics for controlling its operationbefore, during, and after processing of a semiconductor wafer orsubstrate. The electronics is referred to as the “controller,” which maycontrol various components or subparts of the system. The controller,depending on processing requirements and/or a type of the system, isprogrammed to control any process disclosed herein, including a deliveryof process gases, temperature settings (e.g., heating and/or cooling),pressure settings, vacuum settings, power settings, RF generatorsettings, RF matching circuit settings, frequency settings, flow ratesettings, fluid delivery settings, positional and operation settings,wafer transfers into and out of a tool and other transfer tools and/orload locks connected to or interfaced with the system.

Broadly speaking, in a variety of embodiments, the controller is definedas electronics having various integrated circuits, logic, memory, and/orsoftware that receive instructions, issue instructions, controloperation, enable cleaning operations, enable endpoint measurements, andthe like. The integrated circuits include chips in the form of firmwarethat store program instructions, digital signal processors (DSP)s, chipsdefined as ASICs, PLDs, one or more microprocessors, or microcontrollersthat execute program instructions (e.g., software). The programinstructions are instructions communicated to the controller in the formof various individual settings (or program files), defining operationalparameters for carrying out a process on or for a semiconductor wafer.The operational parameters are, in some embodiments, a part of a recipedefined by process engineers to accomplish one or more processing stepsduring the fabrication of one or more layers, materials, metals, oxides,silicon, silicon dioxide, surfaces, circuits, and/or dies of a wafer.

The controller, in some embodiments, is a part of or coupled to acomputer that is integrated with, coupled to the system, otherwisenetworked to the system, or a combination thereof. For example, thecontroller is in a “cloud” or all or a part of a fab host computersystem, which allows for remote access for wafer processing. Thecontroller enables remote access to the system to monitor currentprogress of fabrication operations, examines a history of pastfabrication operations, examines trends or performance metrics from aplurality of fabrication operations, to change parameters of currentprocessing, to set processing steps to follow a current processing, orto start a new process.

In some embodiments, a remote computer (e.g. a server) provides processrecipes to the system over a computer network, which includes a localnetwork or the Internet. The remote computer includes a user interfacethat enables entry or programming of parameters and/or settings, whichare then communicated to the system from the remote computer. In someexamples, the controller receives instructions in the form of settingsfor processing a wafer. It should be understood that the settings arespecific to a type of process to be performed on a wafer and a type oftool that the controller interfaces with or controls. Thus as describedabove, the controller is distributed, such as by including one or morediscrete controllers that are networked together and working towards acommon purpose, such as the fulfilling processes described herein. Anexample of a distributed controller for such purposes includes one ormore integrated circuits on a chamber in communication with one or moreintegrated circuits located remotely (such as at a platform level or aspart of a remote computer) that combine to control a process in achamber.

Without limitation, in various embodiments, the system includes a plasmaetch chamber, a deposition chamber, a spin-rinse chamber, a metalplating chamber, a clean chamber, a bevel edge etch chamber, a physicalvapor deposition (PVD) chamber, a chemical vapor deposition (CVD)chamber, an atomic layer deposition (ALD) chamber, an atomic layer etch(ALE) chamber, an ion implantation chamber, a track chamber, and anyother semiconductor processing chamber that is associated or used infabrication and/or manufacturing of semiconductor wafers.

It is further noted that although the above-described operations aredescribed with reference to a parallel plate plasma chamber, e.g., acapacitive1y coupled plasma chamber, etc., in some embodiments, theabove-described operations apply to other types of plasma chambers,e.g., a plasma chamber including an inductive1y coupled plasma (ICP)reactor, a transformer coupled plasma (TCP) reactor, conductor tools,dielectric tools, a plasma chamber including an electron cyclotronresonance (ECR) reactor, etc. For example, an X MHz RF generator, a YMHz RF generator, and a Z MHz RF generator are coupled to an inductorwithin the ICP plasma chamber.

As noted above, depending on a process operation to be performed by thetool, the controller communicates with one or more of other toolcircuits or modules, other tool components, cluster tools, other toolinterfaces, adjacent tools, neighboring tools, tools located throughouta factory, a main computer, another controller, or tools used inmaterial transport that bring containers of wafers to and from toollocations and/or load ports in a semiconductor manufacturing factory.

With the above embodiments in mind, it should be understood that some ofthe embodiments employ various computer-implemented operations involvingdata stored in computer systems. These computer-implemented operationsare those that manipulate physical quantities.

Some of the embodiments also relate to a hardware unit or an apparatusfor performing these operations. The apparatus is specially constructedfor a special purpose computer. When defined as a special purposecomputer, the computer performs other processing, program execution orroutines that are not part of the special purpose, while still beingcapable of operating for the special purpose.

In some embodiments, the operations, described herein, are performed bya computer selective1y activated, or are configured by one or morecomputer programs stored in a computer memory, or are obtained over acomputer network. When data is obtained over the computer network, thedata may be processed by other computers on the computer network, e.g.,a cloud of computing resources.

One or more embodiments, described herein, can also be fabricated ascomputer-readable code on a non-transitory computer-readable medium. Thenon-transitory computer-readable medium is any data storage hardwareunit, e.g., a memory device, etc., that stores data, which is thereafterread by a computer system. Examples of the non-transitorycomputer-readable medium include hard drives, network attached storage(NAS), ROM, RAM, compact disc-ROMs (CD-ROMs), CD-recordables (CD-Rs),CD-rewritables (CD-RWs), magnetic tapes and other optical andnon-optical data storage hardware units. In some embodiments, thenon-transitory computer-readable medium includes a computer-readabletangible medium distributed over a network-coupled computer system sothat the computer-readable code is stored and executed in a distributedfashion.

Although some method operations, described above, were presented in aspecific order, it should be understood that in various embodiments,other housekeeping operations are performed in between the methodoperations, or the method operations are adjusted so that they occur atslightly different times, or are distributed in a system which allowsthe occurrence of the method operations at various intervals, or areperformed in a different order than that described above.

It should further be noted that in an embodiment, one or more featuresfrom any embodiment described above are combined with one or morefeatures of any other embodiment without departing from a scopedescribed in various embodiments described in the present disclosure.

Although the foregoing embodiments have been described in some detailfor purposes of clarity of understanding, it will be apparent thatcertain changes and modifications can be practiced within the scope ofappended claims. Accordingly, the present embodiments are to beconsidered as illustrative and not restrictive, and the embodiments arenot to be limited to the details given herein, but may be modifiedwithin the scope and equivalents of the appended claims.

1. A tuning method comprising: accessing, for a first set of one or morecycles of operation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator; calculating a plurality of load impedance parameter valuesfrom the plurality of reflection parameter values by applying theplurality of reflection parameter values to a computer-based model of atleast a portion of a radio frequency path, wherein the radio frequencypath is between the second radio frequency generator and an electrode ofa plasma chamber; receiving a plurality of frequency modulationparameters of a radio frequency signal to be generated by the secondradio frequency generator; determining values of the plurality offrequency modulation parameters by applying the plurality of loadimpedance parameter values to the computer-based model, wherein thevalues of the plurality of frequency modulation parameters aredetermined to minimize a reflection coefficient parameter at an input ofthe computer-based model; and controlling the second radio frequencygenerator according to the values of the plurality of frequencymodulation parameters during a second set of one or more cycles ofoperation of the first radio frequency generator.
 2. The method of claim1, wherein said accessing the plurality of reflection parameter values,said calculating the plurality of load impedance parameter values, saiddetermining the values of the frequency modulation parameters, and saidcontrolling the second radio frequency generator are executed duringprocessing of a substrate in the plasma chamber.
 3. The method of claim1, wherein the plurality of reflection parameter values include aplurality of voltage reflection coefficient values, and wherein thereflection coefficient parameter is an average power reflectioncoefficient.
 4. The method of claim 1, wherein the second set of one ormore cycles of operation is subsequent to the first set of one or morecycles of operation.
 5. The method of claim 1, wherein the first setincludes two or more cycles of operation of the first radio frequencygenerator, and wherein each of the plurality of reflection parametervalues is an average of multiple reflection coefficient values that arecomputed over the two or more cycles of the first set.
 6. The method ofclaim 1, further comprising: repeating said accessing the plurality ofreflection parameter values, said calculating the plurality of loadimpedance parameter values, and said determining the values of theplurality of frequency modulation parameters for a third set of one ormore cycles of operation of the first radio frequency generator; andrepeating said controlling the second radio frequency generator during afourth set of one or more cycles of operation of the first radiofrequency generator, wherein the third set is subsequent to the secondset and the fourth set is subsequent to the third set.
 7. The method ofclaim 1, wherein the plurality of reflection parameter values include aplurality of values of complex voltage and current.
 8. The method ofclaim 1, wherein the computer-based model includes a plurality ofcircuit elements, wherein two adjacent ones of the plurality of circuitelements are coupled to each other via a connection, and wherein thecomputer-based model has substantially the same impedance as that of theradio frequency path.
 9. The method of claim 1, wherein thecomputer-based model includes a plurality of circuit elements, whereintwo adjacent ones of the plurality of circuit elements are coupled toeach other via a connection, and wherein the plurality of circuitelements represent a plurality of circuit components of the radiofrequency path and are connected in the same manner as that of theplurality of circuit components of the radio frequency path.
 10. Themethod of claim 1, wherein the radio frequency path includes: a radiofrequency cable that couples the second radio frequency generator with abranch of a match network, the branch, a radio frequency transmissionline that couples the match network with the plasma chamber, and anelectrode of the plasma chamber.
 11. The method of claim 1, furthercomprising determining a capacitance for a match network by applying theplurality of load impedance parameter values to the computer-basedmodel, wherein the match network is coupled between the second radiofrequency generator and the plasma chamber and between the first radiofrequency generator and the plasma chamber.
 12. The method of claim 1,wherein said applying the plurality of load impedance parameter valuesto the computer-based model comprises: backpropagating the plurality ofload impedance parameter values from an output of the computer-basedmodel via the computer-based model to facilitate calculation of a firstplurality of reflection parameter input values at the input of thecomputer-based model, wherein the first plurality of reflectionparameter input values are determined when amounts of the plurality offrequency modulation parameters are available to the computer-basedmodel; calculating a first average of the first plurality of reflectionparameter input values; backpropagating the plurality of load impedanceparameter values from the output of the computer-based model via thecomputer-based model to facilitate calculation of a second plurality ofreflection parameter input values at the input of the computer-basedmodel, wherein the second plurality of reflection parameter input valuesare determined when the values of the plurality of frequency modulationparameters are available to the computer-based model; calculating asecond average of the second plurality of reflection parameter inputvalues; and determining whether the second average is lower than thefirst average.
 13. The method of claim 1, wherein the plurality offrequency modulation parameters that are received describe a periodicfunction associated with one of the one or more cycles of operation ofthe first radio frequency generator.
 14. The method of claim 13, whereinthe periodic function is one of a trapezoidal function, a sinusoidalfunction, a pulsed function, and a sawtooth function.
 15. A tuningmethod comprising: during recipe development, accessing, for a set ofone or more cycles of operation of a first radio frequency generator, aplurality of reflection parameter values associated with a second radiofrequency generator; calculating a plurality of load impedance parametervalues from the plurality of reflection parameter values by applying theplurality of reflection parameter values to a computer-based model of atleast a portion of a radio frequency path, wherein the radio frequencypath is between the second radio frequency generator and an electrode ofa plasma chamber; receiving a plurality of frequency modulationparameters of a radio frequency signal to be generated by the secondradio frequency generator; determining values of the plurality offrequency modulation parameters by applying the plurality of loadimpedance parameter values to the computer-based model, wherein thevalues of the plurality of frequency modulation parameters aredetermined to minimize one or more reflection coefficient parameters atan input of the computer-based model; during processing of a substratewithin another plasma chamber, controlling a third radio frequencygenerator according to the values of the plurality of frequencymodulation parameters determined during the recipe development, whereinsaid controlling the third radio frequency generator is performed duringa set of one or more cycles of operation of a fourth radio frequencygenerator.
 16. The method of claim 15, wherein the one or morereflection coefficient parameters that are minimized during the recipedevelopment include an average power reflection coefficient, and whereinthe plurality of reflection parameter values include a plurality ofvalues of a voltage reflection coefficient.
 17. The method of claim 15,wherein the third radio frequency generator is designated to have thesame frequency of operation as that of the second radio frequencygenerator and the fourth radio frequency generator is designated to havethe same frequency of operation as that of the first radio frequencygenerator.
 18. The method of claim 15, wherein the set of one or morecycles of operation of the first radio frequency generator includes twoor more cycles of operation of the first radio frequency generator, andwherein each of the plurality of reflection parameter values is anaverage of multiple reflection coefficient values that are determinedover the two or more cycles of operation of the first radio frequencygenerator.
 19. The method of claim 15, wherein the plurality ofreflection parameter values include a plurality of values of complexvoltage and current.
 20. The method of claim 15, wherein the pluralityof frequency modulation parameters define a trapezoidal function, or asinusoidal function, or a rectangular function, or a triangularfunction.
 21. The method of claim 15, further comprising determining acapacitance for a match network by applying the plurality of loadimpedance parameter values to the computer-based model, wherein thematch network is coupled between the third radio frequency generator andthe other plasma chamber and between the fourth radio frequencygenerator and the other plasma chamber.
 22. The method of claim 15,wherein said applying the plurality of load impedance parameter valuesto the computer-based model comprises: backpropagating the plurality ofload impedance parameter values from an output of the computer-basedmodel via the computer-based model to calculate a first plurality ofreflection parameter input values at the input of the computer-basedmodel, wherein the first plurality of reflection parameter input valuesare determined when amounts of the plurality of frequency modulationparameters are available to the computer-based model; calculating afirst average of the first plurality of reflection parameter inputvalues; backpropagating the plurality of load impedance parameter valuesfrom the output of the computer-based model via the computer-based modelto calculate a second plurality of reflection parameter input values atthe input of the computer-based model, wherein the second plurality ofreflection parameter input values are determined when the values of theplurality of frequency modulation parameters are available to thecomputer-based model; calculating a second average of the secondplurality of parameter input values; and determining that the secondaverage is lower than the first average.
 23. A tuning method comprising:during recipe development, accessing, for a set of one or more cycles ofoperation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator; calculating a plurality of load impedance parameter valuesfrom the plurality of reflection parameter values by applying theplurality of reflection parameter values to a computer-based model of atleast a portion of a radio frequency path between the second radiofrequency generator and an electrode of a plasma chamber; receiving aplurality of frequency modulation parameters of a radio frequency signalto be generated by the second radio frequency generator, wherein theplurality of frequency modulation parameters include a frequencyvariation of the radio frequency signal; determining values of theplurality of frequency modulation parameters by applying the pluralityof load impedance parameter values to the computer-based model, whereinthe values of the plurality of frequency modulation parameters aredetermined to minimize one or more reflection coefficient parameters atan input of the computer-based model; during processing of a substratewithin another plasma chamber, controlling a third radio frequencygenerator according to the values of the plurality of frequencymodulation parameters determined during the recipe development, whereinsaid controlling the third radio frequency generator includes applyingthe values of the plurality of frequency modulation parameters to abaseline frequency of operation of the third radio frequency generator.24. The method of claim 23, wherein the plurality of frequencymodulation parameters define a trapezoidal function, or a sinusoidalfunction, or a rectangular function, or a triangular function.
 25. Themethod of claim 23, wherein the one or more reflection coefficientparameters that are minimized during the recipe development include anaverage power reflection coefficient, and wherein the plurality ofreflection parameter values include a plurality of values of a voltagereflection coefficient.
 26. The method of claim 23, wherein the baselinefrequency is used to minimize a power-based parameter associated withthe third radio frequency generator.
 27. A tuning method comprising:during recipe development, accessing, for a set of one or more cycles ofoperation of a first radio frequency generator, a plurality ofreflection parameter values associated with a second radio frequencygenerator, wherein each of the plurality of reflection parameter valuescorresponds to a bin of each of the one or more cycles of operation ofthe first radio frequency generator; calculating a plurality of loadimpedance parameter values from the plurality of reflection parametervalues by applying the plurality of reflection parameter values to acomputer-based model of at least a portion of a radio frequency path,wherein the radio frequency path is between the second radio frequencygenerator and an electrode of a plasma chamber; determining values of aplurality of frequency modulation parameters by applying the pluralityof load impedance parameter values to the computer-based model, whereinthe values of the plurality of frequency modulation parameters aredetermined to minimize a plurality of values of a reflection coefficientparameter at an input of the computer-based model for each of the bins;during processing of a substrate within another plasma chamber,controlling a third radio frequency generator according to the values ofthe plurality of frequency modulation parameters determined during therecipe development, wherein said controlling the third frequencygenerator is performed during a set of one or more cycles of operationof a fourth radio frequency generator.
 28. The method of claim 27,wherein the reflection coefficient parameter includes a power reflectioncoefficient parameter.
 29. The method of claim 27, wherein the set ofone or more cycles of operation of the first radio frequency generatorincludes two or more cycles of operation of the first radio frequencygenerator, and wherein each of the plurality of reflection parametervalues is an average of multiple reflection coefficient values that aredetermined over the two or more cycles of operation of the first radiofrequency generator.
 30. The method of claim 27, wherein the pluralityof frequency modulation parameters include an average frequency of aradio frequency signal to be output by the third radio frequencygenerator and a frequency variation of the radio frequency signal to beoutput by the third radio frequency generator, and wherein the frequencyvariation is for each bin of a radio frequency signal to be generated bythe fourth radio frequency generator.
 31. The method of claim 27,wherein the plurality of load impedance parameter values are applied tothe computer-based model to determine a capacitance for a match network,and wherein the match network is coupled between the third radiofrequency generator and the other plasma chamber and between the fourthradio frequency generator and the other plasma chamber.
 32. The methodof claim 27, wherein said applying the plurality of load impedanceparameter values to the computer-based model comprises: backpropagatinga first one of the plurality of load impedance parameter values from anoutput of the computer-based model via the computer-based model tofacilitate calculation of a first reflection parameter input value atthe input of the computer-based model, wherein the first reflectionparameter input value is determined when amounts of the plurality offrequency modulation parameters are available to the computer-basedmodel; backpropagating the first one of the plurality of load impedanceparameter values from the output of the computer-based model via thecomputer-based model to calculate a second reflection parameter inputvalue at the input of the computer-based model, wherein the secondreflection parameter input value is determined when the values of theplurality of frequency modulation parameters are available to thecomputer-based model determining whether the second reflection parameterinput value is lower than the first reflection parameter input value.